WISKUNDIGE GELETTERDHEID
GRAAD 10
NOG OEFENINGE
  
Waarkynlikheid en kans : antwoorde
  
MATHEMATICAL LITERACY
GRADE 10
MORE EXERCISES
  
Probability : answers
  
  
Antwoorde  / Answers  1  
  
    
         1.1  Aantal moontlike uitlomste = 6
  
                en aantal susesvolle uitkomste = 1
  
                               1
                P(2)  =  ──
                               6
                                                         [ V 1.1 ]
  
    
         1.2  Aantal moontlike uitlomste = 6
  
                en aantal susesvolle uitkomste = 1
  
                               1
                P(5)  =  ──
                               6
                                                         [ V 1.2 ]
  
    
         1.3  Aantal moontlike uitlomste = 6
  
                en aantal susesvolle uitkomste = 0
  
                ( Daar is geen nulle op dobbelsteen )
  
                               0
                P(8)  =  ──    =  0
                               6
                                                         [ V 1.3 ]
  
    
         1.4  Aantal moontlike uitlomste = 6
  
                Ewe getalle op steen = 2, 4 en 6
  
                dus aantal susesvolle uitkomste = 3
  
                               3
                P(5)  =  ──
                               6
  
                               1
                P(5)  =  ──   . . . vereenvoudig
                               2
                                                         [ V 1.4 ]
  
    
         1.5  Aantal moontlike uitlomste = 6
  
                Getalle < 4 = 1, 2 en 3
  
                dus aantal susesvolle uitkomste = 3
  
                               3
                P(5)  =  ──
                               6
  
                               1
                P(5)  =  ──   . . . vereenvoudig
                               2
                                                         [ V 1.5 ]
  
    
         1.6  Aantal moontlike uitlomste = 6
  
                Ewe getalle < 3 = 4 en 6
  
                dus aantal susesvolle uitkomste = 2
  
                               2
                P(5)  =  ──
                               6
  
                               1
                P(5)  =  ──   . . . vereenvoudig
                               3
                                                         [ V 1.6 ]
  
    
         1.1  Total probabile outcomes = 6
  
                and total favourable outcomes = 1
  
                              1
                P(2)  =  ──
                              6
                                                         [ Q 1.1 ]
  
    
         1.2  Total probabile outcomes = 6
  
                and total favourable outcomes = 1
  
                              1
                P(5)  =  ──
                              6
                                                         [ Q 1.2 ]
  
    
         1.3  Total probabile outcomes = 6
  
                and total favourable outcomes = 0
  
                ( There are no 8's on a die)
  
                              0
                P(5)  =  ──  =  0
                              6
                                                         [ Q 1.3 ]
  
    
         1.4  Total probabile outcomes = 6
  
                Even numbers on die = 2, 4 and 6.
  
                and thus total favourable outcomes = 3
  
                                                  3
                P(even number)  =  ──
                                                  6
                                                  1
                                            =  ──   . . .  simplify
                                                  2
  
                                                         [ Q 1.4 ]
  
    
         1.5  Total probabile outcomes = 6
  
                Numbers smaller than 4 = 1, 2 and 3.
  
                and thus total favourable outcomes = 3
  
                                                  3
                P(even number)  =  ──
                                                  6
  
                                                  1
                                            =  ──   . . .  simplify
                                                  2
                                                         [ Q 1.5 ]
  
    
         1.5  Total probabile outcomes = 6
  
                Even numbers greater than 3 = 4 and 6.
  
                and thus total favourable outcomes = 2
  
                                                  2
                P(even number)  =  ──
                                                  6
  
                                                  1
                                            =  ──   . . .  simplify
                                                  3
                                                         [ Q 1.6 ]
  
  
Antwoorde  / Answers  2  
  
         2.1  52 kaarte
  
                                                         [ V 2. ]
  
         2.2  4 sesse (2 rooi, 2 swart)
  
                                                         [ V 2. ]
  
         2.3  2 X 13 = 26 kaarte
  
                                                         [ V 2. ]
  
         2.1  52 cards
  
                                                         [ Q 2. ]
  
         2.2  4 sixes (2 red, 2 black)
  
                                                         [ Q 2. ]
  
         2.3  2 X 13 = 26 cards
  
                                                         [ Q 2. ]
  
  
Antwoorde  / Answers  3  
  
    
         3.1  Daar is 52 kaarte in die pak en dus
  
                is totale moontlike uitkomstes = 52
  
                Daar is 4 sesse in die pak en
  
                dus aantal susesvolle uitkomste = 4
  
                                4
                P(6)  =  ───
                               52
  
                                 1
                         =  ───   . . . vereenvoudig
                               13
                                                         [ V 3. ]
  
    
         3.2  Daar is 52 kaarte in die pak en dus
  
                is totale moontlike uitkomstes = 52
  
                Daar is 2 rooi sewes in die pak en
  
                dus aantal susesvolle uitkomste = 2
  
                                       2
                P(rooi 7)  =  ───
                                      52
  
                                       1
                                =  ───   . . . vereenvoudig
                                      26
                                                         [ V 3. ]
  
    
         3.3  Daar is 52 kaarte in die pak en dus
  
                is totale moontlike uitkomstes = 52
  
                Daar is net 1 9 van klawers in die pak en
  
                dus aantal susesvolle uitkomste = 1
  
                                1
                P(9)  =  ───
                               52
  
                                                         [ V 3. ]
  
    
         3.4  Daar is 52 kaarte in die pak en dus
  
                is totale moontlike uitkomstes = 52
  
                Daar is 4 Koninginne in die pak en
  
                dus aantal susesvolle uitkomste = 4
  
                                            4
                P(Koningin)  =  ───
                                           52
  
                                            1
                                     =  ───   . . . vereenvoudig
                                           13
                                                         [ V 3. ]
  
    
         3.5  Daar is 52 kaarte in die pak en dus
  
                is totale moontlike uitkomstes = 52
  
                Daar is 2 swart Konings in die pak en
  
                klawers en skoppens, en dus
  
                die aantal susesvolle uitkomste = 2
  
                                         2
                P(Koning)  =  ───
                                        52
  
                                         1
                                  =  ───   . . . vereenvoudig
                                        13
                                                         [ V 3. ]
  
    
         3.6  Daar is 52 kaarte in die pak en dus
  
                is totale moontlike uitkomstes = 52
  
                Daar is 2 X 4 rooi prent kaarte in die
  
                pak, diamante en hartens, en dus
  
                die aantal susesvolle uitkomste = 8
  
                                                        8
                P(rooi prent kaarte)  =  ───
                                                       52
  
                                                        2
                                                 =  ───   . . . vereenvoudig
                                                       13
                                                               [ V 3. ]
  
    
         3.7  Daar is 52 kaarte in die pak en dus
  
                is totale moontlike uitkomstes = 52
  
                Daar is 2 X 13 swart kaarte in die
  
                pak, klawers en skoppens, en dus
  
                52 - 26 nie swart kaarte en dus
  
                die aantal susesvolle uitkomste = 26
  
                                           26
                P(nie swart)  =  ───
                                           52
  
                                            1
                                     =  ───   . . . vereenvoudig
                                            2
                                                               [ V 3. ]
  
    
         3.8  Daar is 52 kaarte in die pak en dus
  
                is totale moontlike uitkomstes = 52
  
                Daar is geen geel kaarte in die pak nie
  
                en dus aantal susesvolle uitkomste = 0
  
                                              0
                P(geel kaart)  =  ───
                                             52
  
                                      =  0                   [ V 3. ]
  
    
         3.9  Daar is 52 kaarte in die pak en dus
  
                is totale moontlike uitkomstes = 52
  
                Daar is geen rooi 12's in die pak nie
  
                en dus aantal susesvolle uitkomste = 0
  
                                         0
                P(rooi 12)  =  ───
                                        52
  
                                  =  0                      [ V 3. ]
  
    
         3.10  Daar is 52 kaarte in die pak en dus
  
                  is totale moontlike uitkomstes = 52
  
                  Daar is 13 Hartens in die pak
  
                  die aantal susesvolle uitkomste = 13
  
                                           13
                  P(Hartens)  =  ───
                                           52
  
                                            1
                                     =  ───
                                            4
                                                                 [ V 3. ]
  
    
         3.11  Daar is 52 kaarte in die pak en dus
  
                  is totale moontlike uitkomstes = 52
  
                  Daar is 2 X 5 = 10 rooi kaarte
  
                  kleiner as 7 in die pak en dus
  
                  die aantal susesvolle uitkomste = 10
  
                                                    10
                  P(rooi kaart < 7)  =  ───
                                                    52
  
                                                     5
                                              =  ───
                                                    26
                                                                 [ V 3. ]
  
    
         3.12  Daar is 52 kaarte in die pak en dus
  
                  is totale moontlike uitkomstes = 52
  
                  Daar is 4 klawer prent kaarte en
  
                  dus aantal susesvolle uitkomste = 4
  
                                                              4
                  P(klawers prent kaart)  =  ───
                                                             52
  
                                                              1
                                                       =  ───
                                                             13
                                                                 [ V 3. ]
  
    
         3.1  There are 52 cards in the pack.
  
                and thus total probabile outcomes = 52
  
                There are 4 sixes in the pack.
  
                and thus total favourable outcomes = 4
  
                                4
                P(6)  =  ───
                               52
  
                                1
                         =  ───   . . .  simplify
                               13
                                                         [ Q 3. ]
  
    
         3.2  There are 52 cards in the pack.
  
                and thus total probabile outcomes = 52
  
                There are 2 red sevens in the pack.
  
                and thus total favourable outcomes = 2
  
                                      2
                P(red 7)  =  ───
                                     52
  
                                      1
                               =  ───   . . .  simplify
                                     26
                                                         [ Q 3. ]
  
    
         3.3  There are 52 cards in the pack.
  
                and thus total probabile outcomes = 52
  
                There is only 1 9 of spades in the pack.
  
                and thus total favourable outcomes = 1
  
                                1
                P(9)  =  ───
                               52
  
                                                         [ Q 3. ]
  
    
         3.4  There are 52 cards in the pack.
  
                and thus total probabile outcomes = 52
  
                There are 4 Queens in the pack.
  
                and thus total favourable outcomes = 4
  
                                         4
                P(Queen)  =  ───
                                        52
  
                                         1
                                  =  ───   . . .  simplify
                                        13
                                                         [ Q 3. ]
  
    
         3.5  There are 52 cards in the pack.
  
                and thus total probabile outcomes = 52
  
                There are 2 black Kings in the pack,
  
                clubs and spades.
  
                and thus total favourable outcomes = 2
  
                                     2
                P(King)  =  ───
                                    52
  
                                     1
                              =  ───   . . .  simplify
                                    26
                                                         [ Q 3. ]
  
    
         3.6  There are 52 cards in the pack.
  
                and thus total probabile outcomes = 52
  
                There are 2 X 4 red picture cards in
  
                the pack, diamonfs and hearts.
  
                and thus total favourable outcomes = 8
  
                                               8
                P(red picture)  =  ───
                                              52
  
                                               2
                                        =  ───   . . .  simplify
                                              13
                                                         [ Q 3. ]
  
    
         3.7  There are 52 cards in the pack.
  
                and thus total probabile outcomes = 52
  
                There are 2 X 13 black cards in the pack,
  
                clubs and spades and thus 52 - 26
  
                not black cards and thus
  
                total favourable outcomes = 26
  
                                           26
                P(not black)  =  ───
                                           52
  
                                            1
                                     =  ───   . . .  simplify
                                            2
                                                         [ Q 3. ]
  
    
         3.8  There are 52 cards in the pack.
  
                and thus total probabile outcomes = 52
  
                There are no yellow cards in the pack,
  
                and thus total favourable outcomes = 0
  
                                                   0
                P(a yellow card)  =  ───
                                                  52
  
                                             =  0          [ Q 3. ]
  
    
         3.9  There are 52 cards in the pack.
  
                and thus total probabile outcomes = 52
  
                There are no red 12's in the pack,
  
                and thus total favourable outcomes = 0
  
                                           0
                P(a red 12)  =  ───
                                          52
  
                                    =  0                  [ Q 3. ]
  
    
         3.10  There are 52 cards in the pack.
  
                  and thus total probabile outcomes = 52
  
                  There are 13 Hearts in the pack,
  
                  and thus total favourable outcomes = 13
  
                                           13
                  P(a Heart)  =  ───
                                           52
  
                                            1
                                     =  ───
                                            4
                                                             [ Q 3. ]
  
    
         3.11  There are 52 cards in the pack.
  
                  and thus total probabile outcomes = 52
  
                  There are 2 x 5 = 10 red cards smaller
  
                  than 7 in the pack,
  
                  and thus total favourable outcomes = 10
  
                                                  10
                  P(red card < 7)  =  ───
                                                  52
  
                                                   5
                                            =  ───
                                                  26
                                                             [ Q 3. ]
  
    
         3.12  There are 52 cards in the pack.
  
                  and thus total probabile outcomes = 52
  
                  There are 4 clubs picture cards
  
                  and thus total favourable outcomes = 4
  
                                                            4
                  P(clubs picture card)  =  ───
                                                           52
  
                                                            1
                                                     =  ───
                                                           13
                                                             [ Q 3. ]
  
  
Antwoorde  / Answers  4  
  
    
         4.1  Daar is 30 seuns in die klas en dus
  
                is totale moontlike uitkomstes = 30
  
                Daar is 9 wat sokker speel en dus
  
                dus aantal susesvolle uitkomste = 9
  
                                         9
                P(sokker)  =  ───
                                        30
  
                                         3
                                  =  ───   : vereenvoudig
                                        10
                                                         [ V 4. ]
  
    
         4.2  Daar is 30 seuns in die klas en dus
  
                is totale moontlike uitkomstes = 30
  
                Daar is 8 wat krieket speel en dus
  
                dus aantal susesvolle uitkomste = 8
  
                                         8
                P(krieket)  =  ───
                                        30
  
                                         4
                                  =  ───   : vereenvoudig
                                        15
                                                         [ V 4. ]
  
    
         4.3  Daar is 30 seuns in die klas en dus
  
                is totale moontlike uitkomstes = 30
  
                Daar is 9 + 8 + 6 = 23 wat nie rugby
  
                speel nie en dus die aantal
  
                susesvolle uitkomste = 23
  
                  OF  
  
                Daar is 7 wat rugby speel en dus
  
                30 - 7 = 23 wat nie rugby speel nie
  
                en dus die aantal
  
                susesvolle uitkomste = 23
  
                                                   23
                P(nie rugby nie?)  =  ───
                                                   30
  
                                                         [ V 4. ]
  
    
         4.4  Daar is 30 seuns in die klas en dus
  
                is totale moontlike uitkomstes = 30
  
                Daar is 6 wat nie aan sport
  
                deelneem nie en dus is die
  
                aantal susesvolle uitkomste = 6
  
                                            6
                P(nie sport)  =  ───
                                           30
  
                                           1
                                    =  ───   : vereenvoudig
                                          15
                                                         [ V 4. ]
  
    
         4.5  Daar is 30 seuns in die klas en dus
  
                is totale moontlike uitkomstes = 30
  
                Daar is 9 + 8 + 7 = 24 wat aan sport
  
                deelneem en dus is die
  
                aantal susesvolle uitkomste = 24
  
                  OF  
  
                Daar is 6 wat nie aan sport
  
                deelneem nie en dus 30 - 6 = 24
  
                wat aan sport deelneem en dus die
  
                aantal susesvolle uitkomste = 24
  
                                     24
                P(sport)  =  ───
                                     30
  
                                      4
                               =  ───   : vereenvoudig
                                      5
                                                         [ V 4. ]
  
    
         4.1  There are 30 boys in the class. and
  
                thus total probabile outcomes = 30
  
                There are 9 that paly soccer and
  
                thus total favourable outcomes = 9
  
                                        9
                P(soccer)  =  ───
                                       30
  
                                         3
                                  =  ───   : simplify
                                        10
                                                         [ Q 4. ]
  
    
         4.2  There are 30 boys in the class. and
  
                thus total probabile outcomes = 30
  
                There are 8 that play cricket and
  
                thus total favourable outcomes = 8
  
                                        8
                P(cricket)  =  ───
                                       30
  
                                         4
                                  =  ───   : simplify
                                        15
                                                         [ Q 4. ]
  
    
         4.3  There are 30 boys in the class. and
  
                thus total probabile outcomes = 30
  
                There are 9 + 8 + 6 = 23 that do not
  
                play rugby and thus total
  
                favourable outcomes = 23
  
                  OR  
  
                There are 7 that play rugby and thus
  
                30 - 7 = 23 that do not play rugby and
  
                thus total favourable outcomes = 23
  
                                            23
                P(not rugby)  =  ───
                                            30
  
                                                         [ Q 4. ]
  
  
  
    
         4.4  There are 30 boys in the class. and
  
                thus total probabile outcomes = 30
  
                There are 6 that do not play any
  
                sport and thus the total
  
                favourable outcomes = 6
  
                                            6
                P(not sport)  =  ───
                                           30
  
                                            1
                                     =  ───   : simplify
                                            5
                                                         [ Q 4. ]
  
    
         4.5  There are 30 boys in the class. and
  
                thus total probabile outcomes = 30
  
                There are 9 + 8 + 7 = 24 that do play
  
                sport and thus total
  
                favourable outcomes = 24
  
                  OR  
  
                There are 6 that do not play sport and thus
  
                30 - 6 = 24 that do play sport and
  
                thus total favourable outcomes = 24
  
                                            24
                P(any sport)  =  ───
                                            30
  
                                            4
                                     =  ───   : simplify
                                            5
                                                         [ Q 4. ]
  
  
  
  
Antwoorde  / Answers  5  
  
    
         5.1  Daar is 25 + 18 + 2 = 45 voertuie
  
                geparkeer en dus is die totale
  
                moontlike uitkomstes = 45
  
                Daar is 2 vragotors en dus die
  
                aantal susesvolle uitkomste = 2
  
                                               2
                P(vragmotor)  =  ───
                                             45
  
                                                         [ V 5. ]
  
    
         5.2  Daar is 45 voertuie geparkeer
  
                en dus is die totale
  
                moontlike uitkomstes = 45
  
                Daar is 25 motors en dus die
  
                aantal susesvolle uitkomste = 25
  
                                      25
                P(motor)  =  ───
                                      45
  
                                       5
                                =  ───   : vereenvoudig
                                       9
                                                         [ V 5. ]
  
    
         5.3  Daar is 45 voertuie geparkeer
  
                en dus is die totale
  
                moontlike uitkomstes = 45
  
                Daar is 18 taxis geparkeer en
  
                dus 45 - 18 = 27 nie taxis nie
  
                aantal susesvolle uitkomste = 27
  
                OF
  
                Daar is 23 + 2 = 27 nie taxis
  
                geparkeer en dus 27 nie taxis nie
  
                aantal susesvolle uitkomste = 27
  
                                              27
                P(nie taxi nie)  =  ───
                                              45
  
                                               3
                                        =  ───
                                               5
                                                         [ V 5. ]
  
    
         5.4  Daar is 45 voertuie geparkeer
  
                en dus is die totale
  
                moontlike uitkomstes = 45
  
                Daar is 0 busse geparkeer
  
                aantal susesvolle uitkomste = 0
  
                                   0
                P(bus)  =  ───
                                  45
  
                             =  0
                                                         [ V 5. ]
  
    
         5.1  There are 25 + 18 + 2 = 45 vehicles
  
                parked and thus total the
  
                total probabile outcomes = 45
  
                There are 2 lorries and thus the
  
                total favourable outcomes = 2
  
                                     2
                P(lorry)  =  ───
                                    45
  
                                                         [ Q 5. ]
  
    
         5.2  There are 45 vehicles
  
                parked and thus total the
  
                total probabile outcomes = 45
  
                There are 25 cars and thus the
  
                total favourable outcomes = 25
  
                                  25
                P(car)  =  ───
                                  45
  
                                   5
                            =  ───   : simplify
                                   9
                                                         [ Q 5. ]
  
    
         5.3  There are 45 vehicles
  
                parked and thus total the
  
                total probabile outcomes = 45
  
                There are 18 taxis parked and thus
  
                45 - 18 = 27 non taxi vehicles, thus
  
                total favourable outcomes = 27
  
                OR
  
                There are 25 + 2 = 27 non taxis parked
  
                parked and thus = 27 non taxi vehicles,
  
                total favourable outcomes = 27
  
                                            27
                P(not a taxi)  =  ───
                                            45
  
                                             3
                                      =  ───   : simplify
                                             5
                                                         [ Q 5. ]
  
    
         5.4  There are 45 vehicles
  
                parked and thus total the
  
                total probabile outcomes = 45
  
                There are 0 busses and thus the
  
                total favourable outcomes = 0
  
                                    0
                P(bus)  =  ───
                                   45
  
                             =  0
                                                         [ Q 5. ]
  
  
Antwoorde  / Answers  6  
  
    
         6.1  Daar is 35 leerling in die klas
  
                en dus is die totale
  
                moontlike uitkomstes = 35
  
                Daar is 19 dogters in die klas
  
                en dus is die totale aantal
  
                susesvolle uitkomste = 19
  
                                       19
                P(dogter)  =  ───
                                       35
  
                                                         [ V 6. ]
  
    
         6.2  Daar is 35 leerling in die klas
  
                en dus is die totale
  
                moontlike uitkomstes = 35
  
                Daar is 15 leerlinge wat tennis
  
                speel en dus is die totale aantal
  
                susesvolle uitkomste = 15
  
                                      15
                P(tennis)  =  ───
                                      35
  
                                       3
                                =  ───
                                       7
                                                         [ V 6. ]
  
    
         6.3  Daar is 35 leerling in die klas
  
                en dus is die totale
  
                moontlike uitkomstes = 35
  
                Daar is 11 - 6 = 5 dogters wat krieket
  
                speel en dus is die totale aantal
  
                susesvolle uitkomste = 5
  
                                                       5
                P(dogter + krieket)  =  ───
                                                      35
  
                                                       1
                                                =  ───
                                                       7
                                                         [ V 6. ]
  
    
         6.4  Daar is 35 leerling in die klas
  
                en dus is die totale
  
                moontlike uitkomstes = 35
  
                Daar is 9 - 3 = 6 seuns wat nie
  
                aan sport deelneem nie
  
                en dus is die totale aantal
  
                susesvolle uitkomste = 6
  
                                                       6
                P(seun + nie sport)  =  ───
                                                      35
  
                                                         [ V 6. ]
  
    
         6.5  Daar is 35 leerling in die klas
  
                en dus is die totale
  
                moontlike uitkomstes = 35
  
                Daar is 9 leerlinge wat nie
  
                aan sport deelneem nie
  
                en dus is die totale aantal
  
                susesvolle uitkomste = 9
  
                                            9
                P(nie sport)  =  ───
                                           35
  
                                                         [ V 6. ]
  
    
         6.6  Daar is 35 leerling in die klas
  
                en dus is die totale
  
                moontlike uitkomstes = 35
  
                Daar is 0 leerlinge wat
  
                sokker speel en dus is die
  
                totale aantal
  
                susesvolle uitkomste = 0
  
                                         0
                P(sokker)  =  ───
                                        35
  
                                 =  0
                                                         [ V 6. ]
  
    
         6.7  Daar is 35 leerling in die klas
  
                en dus is die totale
  
                moontlike uitkomstes = 35
  
                Daar is 11 leerlinge wat
  
                krieket speel en dus is daar
  
                35 - 11 = 24 wat nie krieket
  
                speel nie en dus is die
  
                totale aantal
  
                susesvolle uitkomste = 24
  
                OF
  
                Daar is 15 + 9 = 24 leerlinge
  
                wat nie krieket speel nie en
  
                dus is die totale aantal
  
                susesvolle uitkomste = 24
  
                                        24
                P(sokker)  =  ───
                                        35
  
                                                         [ V 6. ]
  
    
         6.1  There are 35 pupils in the class
  
                and thus the total
  
                probabile outcomes = 35
  
                There are 19 girls in the class
  
                and thus the
  
                total favourable outcomes = 19
  
                                  19
                P(girl)  =  ───
                                  35
  
                                                         [ Q 6. ]
  
    
         6.2  There are 35 pupils in the class
  
                and thus the total
  
                probabile outcomes = 35
  
                There are 15 pupils that play
  
                tennis and thus the
  
                total favourable outcomes = 15
  
                                       15
                P(tennis)  =  ───
                                       35
  
                                       3
                                =  ───   : simplify
                                       5
                                                         [ Q 6. ]
  
    
         6.3  There are 35 pupils in the class
  
                and thus total the
  
                total probabile outcomes = 35
  
                There are 11 - 6 = 5 girls that
  
                play cricket and thus the
  
                total favourable outcomes = 5
  
                                                  5
                P(girl + cricket)  =  ───
                                                 35
  
                                                  3
                                           =  ───   : simplify
                                                  5
                                                         [ Q 6. ]
  
    
         6.4  There are 35 pupils in the class
  
                and thus the total the
  
                probabile outcomes = 35
  
                There are 9 - 3 = 6 boys that
  
                do not play any sport and thus the
  
                total favourable outcomes = 6
  
                                                     6
                P(boy + no sport)  =  ───
                                                    35
  
  
  
                                                         [ Q 6. ]
  
    
         6.5  There are 35 pupils in the class
  
                and thus the total
  
                probabile outcomes = 35
  
                There are 9 pupils that do not
  
                play any sport and thus the
  
                total favourable outcomes = 9
  
  
                                           9
                P(no sport)  =  ───
                                          35
  
  
  
                                                         [ Q 6. ]
  
    
         6.6  There are 35 pupils in the class
  
                and thus the total
  
                probabile outcomes = 35
  
                There are 0 pupils that play
  
                soccer and thus the
  
                total favourable outcomes = 0
  
  
                                         0
                P(soccer)  =  ───
                                        35
  
                                 =  0
                                                         [ Q 6. ]
  
    
         6.7  There are 35 pupils in the class
  
                and thus the total
  
                probabile outcomes = 35
  
                There are 11 pupils that play
  
                cricket and thus there is
  
                35 - 11 = 24 that do not play cricket
  
                and thus the total
  
                favourable outcomes = 24
  
  
  
                OR
  
                There are 15 + 9 = 24 pupils that do
  
                not play cricket and thus
  
                the total
  
                favourable outcomes = 24
  
                                              24
                P(not cricket)  =  ───
                                              35
  
                                                         [ Q 6. ]
  
  
Antwoorde  / Answers  7  
  
    
         7.1  Daar is 10 balle in die sak en
  
                en dus is die totale
  
                moontlike uitkomstes = 10
  
                Daar is 3 blou balle in die sak
  
                en dus is die totale aantal
  
                susesvolle uitkomste = 3
  
                                    3
                P(blou)  =  ───
                                   10
  
                                                         [ V 7. ]
  
    
         7.2  Daar is 10 balle in die sak en
  
                en dus is die totale
  
                moontlike uitkomstes = 10
  
                Daar is 2 geel balle in die sak
  
                en dus is die totale aantal
  
                susesvolle uitkomste = 2
  
                                     2             1
                P(geel)  =  ───    =  ──
                                    10            5
  
                                                         [ V 7. ]
  
    
         7.3  Totale moontlike uitkomste = 10
  
                Daar is 4 rooi balle in die sak
  
                en dus is die totale aantal
  
                susesvolle uitkomste = 4
  
                                    4             2
                P(rooi)  =  ───    =  ──
                                   10            5
  
                                                         [ V 7. ]
  
    
         7.4  Totale moontlike uitkomste = 10
  
                Daar is geen groen balle in die sak
  
                nie en dus is die totale aantal
  
                susesvolle uitkomste = 0
  
                                       0
                P(groen)  =  ───    =  0
                                      10
  
                                                         [ V 7. ]
  
    
         7.5  Totale moontlike uitkomste = 10
  
                Daar is 1 wit, 3 blou en 4 rooi balle
  
                in die sak en dus is die totale aantal
  
                susesvolle uitkomste = 8
  
                                          8             4
                P(nie geel)  =  ───    =  ──
                                         10            5
  
                                                         [ V 7. ]
  
  
OF

               Totale moontlike uitkomste = 10
  
                Daar is 2 geel balle in die sak en
  
                dus is daar 10 - 2 = 8 nie geel
  
                balle in die sak en is die totale
  
                aantal susesvolle uitkomste = 8
  
                                          8             4
                P(nie geel)  =  ───    =  ──
                                         10            5
  
                                                         [ V 7. ]
  
  
OF

                P(nie geel)  =  1  ─  P(geel)
  
                                                   2
                P(nie geel)  =  1  ─  ───
                                                  10
  
                                          8             4
                                   =  ───    =  ──
                                         10            5
  
                                                         [ V 7. ]
  
    
         7.6  Totale moontlike uitkomste = 10
  
                Daar is 1 wit bal in die sak
  
                en dus is die totale aantal
  
                susesvolle uitkomste = 1
  
                                  1
                P(wit)  =  ───
                                 10
  
                                                         [ V 7. ]
  
    
         7.7  Daar is nou geen wit balle
  
                in die sak nie.
  
                                                         [ V 7. ]
  
    
         7.8  Daar is 9 balle in die sak sodat
  
                totale moontlike uitkomste = 9
  
                                                         [ V 7. ]
  
    
         7.9  Die waarskynlikheid sal groter word
  
                omdat daar minder balle in die sak is
  
                maar die aantal blou balle bly dieselfde.
  
                [Die teller bly dieselfde maar die
  
                noemer word kleiner en dus
  
                word die breuk groter]
  
                                                         [ V 7. ]
  
    
         7.10  Totale moontlike uitkomste = 9
  
                  Daar is 3 blou balle in die sak
  
                  en dus is die totale aantal
  
                  susesvolle uitkomste = 3
  
                                       3            1
                  P(blou)  =  ───    =  ──
                                       9            3
  
                  Dit bevestig my antwoord in 7.9.
  
                                                         [ V 7. ]
  
    
         7.11  Totale moontlike uitkomste = 9
  
                  Daar is geen wit balle in die sak
  
                  nie en dus is die totale aantal
  
                  susesvolle uitkomste = 0
  
                                    0
                  P(wit)  =  ───    =  0
                                    9
  
                                                         [ V 7. ]
  
    
         7.12  Totale moontlike uitkomste = 9
  
                  Daar is 4 rooi balle in die sak
  
                  en dus is die totale aantal
  
                  susesvolle uitkomste = 4
  
                                      4
                  P(rooi)  =  ───
                                      9
  
                                                         [ V 7. ]
  
    
         7.1  There are 10 balls in the bag
  
                and thus the total
  
                probabile outcomes = 10
  
                There are 3 blue balls in the bag
  
                and thus the
  
                total favourable outcomes = 3
  
                                    3
                P(blue)  =  ───
                                   10
  
                                                         [ Q 7. ]
  
    
         7.2  There are 10 balls in the bag
  
                and thus the total
  
                probabile outcomes = 10
  
                There are 2 yellow balls in the bag
  
                and thus the
  
                total favourable outcomes = 2
  
                                        2             1
                P(yellow)  =  ───    =  ──
                                       10            5
  
                                                         [ Q 7. ]
  
    
         7.3  Total probabile outcomes = 10
  
                There are 4 red balls in the bag
  
                and thus the
  
                total favourable outcomes = 4
  
                                   4             2
                P(red)  =  ───    =  ──
                                  10            5
  
                                                         [ Q 7. ]
  
    
         7.4  Total probabile outcomes = 10
  
                There no green balls in the bag
  
                and thus the
  
                total favourable outcomes = 0
  
                                       0
                P(green)  =  ───    =  0
                                      10
  
                                                         [ Q 7. ]
  
    
         7.5  Total probabile outcomes = 10
  
                There are 1 white, 3 blue and 4 red
  
                balls in the bag and thus the
  
                total favourable outcomes = 8
  
                                              8             4
                P(not yellow)  =  ───    =  ──
                                             10            5
  
                                                         [ Q 7. ]
  
  
OR

                Total probabile outcomes = 10
  
                There are 2 yellow balls in the bag
  
                thus there are 10 ─ 2 = 8 not yellow
  
                balls in the bag and thus the
  
                total favourable outcomes = 8
  
                                              8             4
                P(not yellow)  =  ───    =  ──
                                             10            5
  
                                                         [ Q 7. ]
  
  
OR

                P(not yellow)  =  1 ─ P(yellow)
  
                                                    2
                P(not yellow)  =  1 ─ ───
                                                   10
  
                                              8             4
                                       =  ───    =  ──
                                             10            5
  
                                                         [ Q 7. ]
  
    
         7.6  Total probabile outcomes = 10
  
                There is 1 white ball in the bag
  
                and thus the
  
                total favourable outcomes = 1
  
                                      1
                P(white)  =  ───
                                     10
  
                                                         [ Q 7. ]
  
    
         7.7  There are now no white balls
  
                in the bag.
  
                                                         [ Q 7. ]
  
    
         7.8  There are 9 balls in the bag so that
  
                total favourable outcomes = 9
  
                                                         [ Q 7. ]
  
    
         7.9  The probability will increase because
  
                there are fewer balls in the bag but the
  
                number of blue balls remained the same.
  
                [The numerator remained the same
  
                but the denominator increased and
  
                thus the fraction becomes greater.]
  
                                                         [ Q 7. ]
  
    
         7.10  Total probabile outcomes = 9
  
                  There are 3 blue balls in the bag
  
                  and thus the
  
                  total favourable outcomes = 3
  
                                      3             1
                  P(blue)  =  ───    =  ──
                                      9             3
  
                  This confirms my answer in 7.9.
  
                                                         [ Q 7. ]
  
    
         7.11  Total probabile outcomes = 9
  
                  There no white balls in the bag
  
                  and thus the
  
                  total favourable outcomes = 0
  
                                         0
                  P(green)  =  ───    =  0
                                        10
  
                                                         [ Q 7. ]
  
    
         7.12  Total probabile outcomes = 9
  
                  There 4 red balls in the bag
  
                  and thus the
  
                  total favourable outcomes = 4
  
                                     4
                  P(red)  =  ───
                                     9
  
                                                         [ Q 7. ]
  
  
Antwoorde  / Answers  8  
  
    
         8.1  A  =  150  ─  (36 + 46 + 19)      
  
                    =  49                                  [ V/Q 8. ]
  
  
  
  
  
  
  
    
         8.1  C  =  36  +  57
  
                    =  93                                   [ V/Q 8. ]
  
    
         8.1  E  =  19  +  14
  
                    =  33                                   [ V/Q 8. ]
  
    
         8.2.1  Die totale aantal leerlinge is 280
  
                   en dus is die totale
  
                   moontlike uitkomstes = 280
  
                   82 leerlinge kom per motor en dus
  
                   totale susesvolle uitkomste = 82
  
                                               82             41
                   P(per motor)  =  ───    =  ───
                                              280          140
  
                                                         [ V 8. ]
  
    
         8.2.2  Die totale aantal Graad 8
  
                   leerlinge is 150
  
                   totale moontlike uitkomstes = 150
  
                   19 Graad 8's kom per taxi en dus
  
                   totale susesvolle uitkomste = 19
  
                                                19
                   P(8 per taxi)  =  ────
                                               150
  
                                                         [ V 8. ]
  
    
         8.2.3  Die totale aantal Graad 9
  
                   leerlinge is 130
  
                   totale moontlike uitkomstes = 130
  
                   26 Graad 9's kom per bus en dus
  
                   totale susesvolle uitkomste = 26
  
                                                26               1
                   P(9 per bus)  =  ────    =  ───
                                               130              5
  
                                                         [ V 8. ]
  
    
         8.2.4  Die totale aantal Graad 8
  
                   leerlinge is 150
  
                   totale moontlike uitkomstes = 150
  
                   36 Graad 8's het gestap en dus
  
                   totale susesvolle uitkomste = 36
  
                                              36              6
                   P(8 + stap)  =  ────    =  ───
                                             150            25
  
                                                         [ V 8. ]
  
    
         8.2.5  Die totale aantal Graad 9
  
                   leerlinge is 130
  
                   totale moontlike uitkomstes = 130
  
                   Geen Graad 9's het gefiets nie en dus
  
                   totale susesvolle uitkomste = 0
  
                                                  0
                   P(9 per fiets)  =  ────    =  0
                                                130
  
                                                         [ V 8. ]
  
    
         8.2.1  Die totale aantal leerlinge is 280
  
                   en dus is die totale
  
                   moontlike uitkomstes = 280
  
                   Geen leerling kom per treim en dus
  
                   totale susesvolle uitkomste = 0
  
                                              0
                   P(per trein)  =  ───    =  0
                                            280
  
                                                         [ V 8. ]
  
    
         8.1  B  =  130  ─  (57 + 26 + 14)      
  
                    =  33                                    [ V/Q 8. ]
  
                               OF / OR
  
                B  =  82  ─  49    . . . A
  
                    =  33                                    [ V/Q 8. ]
  
    
         8.1  D  =  46  +  26
  
                    =  72                                    [ V/Q 8. ]
  
    
         8.1  F  =  150  +  130
  
                    =  280                                  [ V/Q 8. ]
  
    
         8.2.1  The total number of pupils is 280
  
                   and thus the total
  
                   probabile outcomes = 280
  
                   82 pupils came by car and thus
  
                   the total favourable outcomes = 82
  
                                           82               41
                   P(by car)  =  ────    =  ────
                                          280             140
  
                                                                       [ Q 8. ]
  
    
         8.2.2  The total number of Grade 8
  
                   pupils is 150
  
                   total probabile outcomes = 150
  
                   19 Grade 8 pupils came by taxi and
  
                   thus total favourable outcomes = 19
  
                                                19
                   P(8 by taxi)  =  ─────
                                               150
  
                                                                       [ Q 8. ]
  
    
         8.2.3  The total number of Grade 9
  
                   pupils is 130
  
                   total probabile outcomes = 130
  
                   26 Grade 9 pupils came by bus and
  
                   thus total favourable outcomes = 26
  
                                               26                1
                   P(9 by bus)  =  ─────    =  ───
                                              130               5
  
                                                                       [ Q 8. ]
  
    
         8.2.4  The total number of Grade 8
  
                   pupils is 150
  
                   total probabile outcomes = 150
  
                   36 Grade 8 pupils walked and
  
                   thus total favourable outcomes = 36
  
                                               36                6
                   P(8 + walk)  =  ─────    =  ───
                                              150              25
  
                                                                       [ Q 8. ]
  
    
         8.2.5  The total number of Grade 9
  
                   pupils is 130
  
                   total probabile outcomes = 130
  
                   No Grade 9 pupils bicycled to school
  
                   thus total favourable outcomes = 0
  
                                                     0
                   P(9 by bicycle)  =  ─────    =  0
                                                   130
  
                                                                       [ Q 8. ]
  
    
         8.2.6  The total number of pupils is 280
  
                   and thus the total
  
                   probabile outcomes = 280
  
                   No pupils came by train and thus
  
                   the total favourable outcomes = 0
  
                                              0
                   P(by train)  =  ────    =  0
                                            280
  
                                                                       [ Q 8. ]
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
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