WISKUNDIGE GELETTERDHEID
GRAAD 12
NOG OEFENINGE
  
Waarskynlikheid.
  
MATHEMATICAL LITERACY
GRADE 12
MORE EXERCISES
  
Probability
  
  
Vraag  / Question  1  
  
         'n Houer met gegeurde lekkers bevat
         14 pynappel, 8 kersie, 12 koejawel en
         6 appelkoos gegeurde lekkers.
         'n Lekkker word ewekansig gekies.
         Wat is die waarskynlikheid dat
         die gekose lekker
  
         1.1  'n pynappel geur het?
                                                           [ A 1.1 ]
         1.2  'n appelkoos geur het?
                                                           [ A 1.2 ]
         1.3  'n koejawel geur het?
                                                           [ A 1.3 ]
         1.4  nie 'n koejawel geur het nie?
                                                           [ A 1.4 ]
         1.5  nie 'n pynappel geur het nie?
                                                           [ A 1.5 ]
         1.6  nie 'n kersie geur het nie?
                                                           [ A 1.6 ]
         1.7  'n lemoen geur het?
                                                           [ A 1.7 ]
         1.8  nie 'n lemoen geur het nie?
                                                           [ A 1.8 ]
         A tin containing flavoured sweets contains
         14 pineapple, 8 cherry, 12 guava and
         6 apricot flavoured sweets.
         A sweet is selected randomly.
         What is the probability that
         the chosen sweet wiil
  
         1.1  have a pineapple flavour?
                                                           [ A 1.1 ]
         1.2  have an apricot flavour?
                                                           [ A 1.2 ]
         1.3  have a guava flavour?
                                                           [ A 1.3 ]
         1.4  not have a guava flavour?
                                                           [ A 1.4 ]
         1.5  not have a pineapple flavour?
                                                           [ A 1.5 ]
         1.6  not have a cherry flavour?
                                                           [ A 1.6 ]
         1.7  have an orange flavour?
                                                           [ A 1.7 ]
         1.8  not have an orange flavour?
                                                           [ A 1.8 ]
  
Vraag  / Question  2  
  
         Jy trek 'n kaart uit 'n pak van 52 goed
         geskommelde kaarte en nadat jy
         noteer het watter kaart dit is,
         plaas jy dit terug.
         Wat is die waarskynlikheid dat
         die kaart
  
         2.1  die konigin (of vrou) van
                skoppens is?
                                                           [ A 2.1 ]
  
         2.2  'n swart kaart is?
                                                           [ A 2.2 ]
  
         2.3  'n diamant (of ruitens) is?
                                                           [ A 2.3 ]
  
         2.4  'n rooi prent kaart is?
                                                           [ A 2.4 ]
  
         2.5  nie 'n rooi prent kaart nie is?
                                                           [ A 2.5 ]
  
         2.6  nie 'n prent kaart nie is?
                                                           [ A 2.6 ]
  
         2.7  'n swart genommerde kaart is?
                                                           [ A 2.7 ]
  
         2.8  'n boer is?
                                                           [ A 2.8 ]
  
         2.9  'n swart genommerde kaart met
                'n nommer kleiner as 8 maar
                groter as 4 is?
                                                           [ A 2.9 ]
  
         2.10  'n rooi genommerde kaart
                  met 'n nommer kleiner as 7 is?
                                                           [ A 2.10 ]
  
         2.11  'n swart prent kaart is?
                                                           [ A 2.11 ]
  
         2.12  nie 'n rooi genommerde kaart
                  is nie?
                                                           [ A 2.10 ]
  
         2.13  nie 'n aas is nie?
                                                           [ A 2.13 ]
  
         You withdraw a card from a well shuffled
         pack of 52 playing cards and after noticing
         what card it is, you replace it.
         What is the probability that this card will
  
  
  
         2.1  be the queen of spades?
                                                           [ A 2.1 ]
  
  
         2.2  be a black card?
                                                           [ A 2.2 ]
  
         2.3  be a diamond?
                                                           [ A 2.3 ]
  
         2.4  be a red picture card?
                                                           [ A 2.4 ]
  
         2.5  not be a red picture card?
                                                           [ A 2.5 ]
  
         2.6  not be a picture card?
                                                           [ A 2.6 ]
  
         2.7  be a black numbered card?
                                                           [ A 2.7 ]
  
         2.8  be a jack?
                                                           [ A 2.8 ]
  
         2.9  be a numbered card with a number
                smaller than 8 but greater than 4?
                                                           [ A 2.9 ]
  
  
         2.10  be a red numbered card with a number
                  smaller than 7?
                                                           [ A 2.10 ]
  
         2.11  be a black picture card?
                                                           [ A 2.11 ]
  
         2.12  not be a red numbered card?
                                                           [ A 2.12 ]
  
  
         2.13  not be an ace?
                                                           [ A 2.13 ]
  
  
Vraag  / Question  3  
  
         Die tabel hieronder toon hoeveel
         Graad 12 leerlinge hulle
         Wiskundige Geletterdheid huiswerk
         gedoen het - seuns en dogters
         afsonderlik.
         You withdraw a card from a well shuffled
         The table below shows how many
         Grade 12 students did their Mathematical
         Literacy homework - boys and girls separately.
  
  
  
  
Seuns / Boys
  
Dogters / Girls
  
Huiswerk gedoen / Homework done
  
6
  
16
  
Huiswerk nie gedoen nie / Homework not done
  
11
  
7
  
  
         3.1  Hoeveel leerlinge is daar in
                die klas?
                                                           [ A 3.1 ]
  
         3.2  Bepaal die waarskynlikheid dat
                'n willekeurig gekose leerling
  
         3.2.1  'n dogter sal wees.        [ A 3.2.1 ]
  
         3.2.2  'n seun sal wees wat sy
                   huiswerk gedoen het.
                                                         [ A 3.2.2 ]
  
         3.2.3  'n dogter sal wees wat nie
                   haar huiswerk gedoen het nie.
                                                         [ A 3.2.3 ]
  
         3.2.4  'n leerling sal wees wat nie
                   die huiswerk gedoen het nie.
                                                         [ A 3.2.4 ]
  
         3.2.5  'n Graad 11 leerling sal wees.
                                                         [ A 3.2.5 ]
  
         3.3  'n Dogter word willekeurig gekies.
                Bereken die waarskynlikheid
                dat hierdie dogter nie haar
                huiswerk gedoen het nie.
                                                           [ A 3.3 ]
  
         3.4  'n Seun word willekeurig gekies.
                Bereken die waarskynlikheid
                dat hierdie seun sy huiswerk
                gedoen het.
                                                           [ A 3.4 ]
  
         3.1  How many students are there in
                the class?
                                                           [ A 3.1 ]
  
         3.2  Determine the probability that a
                randomly chosen student will be
   
         3.2.1  a girl.                            [ A 3.2.1 ]
  
         3.2.2  a boy that has done his
                   homework.                   [ A 3.2.2 ]
  
  
         3.2.3  a girl that has not done her
                   homework.                   [ A 3.2.3 ]
  
  
         3.2.4  a student that has not done the
                   homework.                   [ A 3.2.4 ]
  
  
         3.2.5  a Grade 11 student.     [ A 3.2.5 ]
  
  
         3.3  A girl is chosen randomly.
                Calculate the probability that
                this girl will not have done
                her homework.
                                                           [ A 3.3 ]
  
         3.4  A boy is chosen randomly.
                Calculate the probability that
                this boy will have done
                his homework.
                                                           [ A 3.4 ]
  
  
  
Vraag  / Question  4  
  
         Elf kaarte word uitgesny. Op elke
         kaart word een van die letters
         van die woord "Suid-Afrika" geskryf,
         soos hieronder vertoon.
         Eleven cards are made. On each card
         is written a letter of the word
         "Suid-Afrika", as shown below.
  
 
 
         'n Kaart word willekeurig gekies.
         Bereken die waarskynlikheid dat
         die letter op die kaart
  
         4.1  'n D is.                                  [ A 4.1 ]
  
         4.2  'n K is.                                  [ A 4.2 ]
  
         4.3  'n klinker is.                          [ A 4.3 ]
  
         4.4  'n konsonant is.                    [ A 4.4 ]
  
         4.5  'n A is.                                  [ A 4.5 ]
  
         4.6  'n B is.                                  [ A 4.6 ]
  
         4.7  nie 'n O is nie.                      [ A 4.7 ]
  
         4.8  nie 'n F is nie.                      [ A 4.8 ]
  
         4.9  nie 'n E is nie.                      [ A 4.9 ]
  
         4.10  nie 'n I is nie.                     [ A 4.10 ]
  
         4.11  nie 'n klinker is nie.            [ A 4.11 ]
  
         A card is chosen randomly.
         Calculate the ptobability that
         the letter on the card will
  
         4.1  be a D.                               [ A 4.1 ]
  
         4.2  be a K.                               [ A 4.2 ]
  
         4.3  be a vowel.                        [ A 4.3 ]
  
         4.4  be a consonant.                 [ A 4.4 ]
  
         4.5  be an A.                             [ A 4.5 ]
  
         4.6  be a B.                               [ A 4.6 ]
  
         4.7  not be an O.                       [ A 4.7 ]
  
         4.8  not be an F.                        [ A 4.8 ]
  
         4.9  not be an E.                        [ A 4.9 ]
  
         4.10  not be an I.                        [ A 4.10 ]
  
         4.11  not be a consonant.          [ A 4.11 ]
  
  
Vraag  / Question  5  
  
         Tien identiese balle word van
         1 tot 10 genommer en dan in
         'n sak geplaas.
         'n Bal word willekeurig uit die sak
         getrek, die nommer neergeskryf
         en dan weer in die sak geplaas.
         Wat is die waarskynlikheid dat
         die nommer op die gekose bal
  
         5.1  'n 5 is?                                  [ A 5.1 ]
  
         5.2  'n ewe getal is?                     [ A 5.2 ]
  
         5.3  'n sysfer kleiner as 6 sal hê?
                                                              [ A 5.3 ]
  
         5.4  'n onewe getal groter as 3 is?
                                                              [ A 5.4 ]
  
         5.5  'n veelvoud van 3 is?             [ A 5.5 ]
  
         5.6  groter of gelyk aan 7 sal wees?
                                                              [ A 5.6 ]
  
         5.7  deelbaar deur 4 is?               [ A 5.7 ]
  
         Bal nommer 4 word uit die sak
         verwyder. Bereken die
         waarskynlikheid dat die nommer
         op die bal
  
         5.8  'n 2 is.                                   [ A 5.8 ]
  
         5.9  'n syfer groter as 3 is.          [ A 5.9 ]
  
         Ten identical balls are numbered from
         1 to 10 and then placed in a bag.
         A ball is withdrawn randomly,
         its number is written down
         and then replaced in the bag.
         What is the probability that
         the number on this ball will
  
  
         5.1  be a 5?                               [ A 5.1 ]
  
         5.2  be an even number?           [ A 5.2 ]
  
         5.3  be a number smaller than 6?
                                                             [ A 5.3 ]
  
         5.4  be an uneven number greater than 3?
                                                             [ A 5.4 ]
  
         5.5  be a multiple of 3?                 [ A 5.5 ]
  
         5.6  be greater than or equal to 7?
                                                             [ A 5.6 ]
  
         5.7  be divisible by 4?                 [ A 5.7 ]
  
         Ball number 4 is removed from the bag.
         Calculate the probability that the
         number of the ball drawn will
  
  
         5.8  be a 2.                               [ A 5.8 ]
  
         5.9  be a number greater than 3.
                                                             [ A 5.9 ]
  
  
Vraag  / Question  6  
  
         Twaalf kinders kyk TV vir 'n
         sekere aantal ure per week.
         Die aantal ure is 2, 12, 4, 3,
         8, 21, 30, 3, 5, 6, 9 en 17.
  
         6.1  Bereken die gemiddelde, mediaan
                en modus van die aantal ure
                wat die kinders TV kyk.
                                                              [ A 6.1 ]
  
         6.2  'n Kind word willekeurig gekies.
                Bereken die waarskynlikheid dat
                die gekose kind na die TV sal kyk vir
  
         6.2.1  3 ure.                                 [ A 6.2.1 ]
  
         6.2.2  6 of meer ure per week.
                                                             [ A 6.2.2 ]
  
         6.2.3  10 of minder ure per week.
                                                             [ A 6.2.3 ]
  
         6.2.4  minder as 3 uur per dag.
                                                             [ A 6.2.4 ]
  
         6.2.5  minder as die gemiddelde
                   ure per week.                    [ A 6.2.5 ]
  
         6.2.6  meer as die mediaan
                   ure per week.                    [ A 6.2.6 ]
  
         6.2.7  die modus ure per week,
                                                              [ A 6.2.7 ]
  
         Twelve children watch TV for a certain
         amount of hours per week.
         The number of hours are 2, 12, 4, 3,
         8, 21, 30, 3, 5, 6, 9 and 17.
  
         6.1  Calculte the mean, median and
                modus of the number of hours
                that the children watch TV,
                                                           [ A 6.1 ]
  
         6.2  A child is chosen randomly.
                Calculate the probability that
                this child will watch TV for
  
         6.2.1  3 hours.                        [ A 6.2.1 ]
  
         6.2.2  6 or more hours per week.
                                                        [ A 6.2.2 ]
  
         6.2.3  10 or less hours per week.
                                                        [ A 6.2.3 ]
  
         6.2.4  less than 3 hours per day.
                                                        [ A 6.2.4 ]
  
         6.2.5  less than the mean hours per week.
                                                        [ A 6.2.5 ]
  
         6.2.6  more than the median hours
                   per week.                     [ A 6.2.6 ]
  
         6.2.7  the modus hours per week.
                                                        [ A 6.2.7 ]
  
  
Vraag  / Question  7  
  
         In 'n sekere skool is die
         waarskynlikheid dat 'n leerling
         sal druip 0,35.
  
         7.1  Wat is die waarskynlikheid
                dat 'n leerling sal slaag?
                                                              [ A 7.1 ]
  
         7.2  Hoeveel leerlinge in 'n klas
                van 74 sal druip?
                                                              [ A 7.2 ]
  
         7.3  Hoeveel leerlinge in 'n klas
                van 132 sal slaag?
                                                              [ A 7.3 ]
  
         In a certain school the probability that
         a pupil wil fail is 0,35.
  
  
         7.1  What is the probability that a
                pupil will pass?
                                                           [ A 7.1 ]
  
         7.2  How many pupils in a class of
                74 will fail?
                                                           [ A 7.2 ]
  
         7.3  How many pupils in a class of
                132 will pass?
                                                           [ A 7.2 ]
  
  
Vraag  / Question  8  
  
  
  
  
         Die diagram aan die regterkant
         toon 'n vierkantige draaibord.
  
         The accompanting diagram on the
         right shows a square spinner.
  
  
 
 
         8.1  Wat is die waarskynlikheid dat
                die draaibord op die kant sal
                land wat met 'n "3" gemerk is?
                                                              [ A 8.1 ]
  
         8.2  P(1) = P(2) = P(3) = P(4).
                Is hierdie stelling korrek?
                Verduidelik.
                                                              [ A 8.2 ]
  
         8.3  Tom dink dat die draaibord
                nie gebalanseerd is nie.
                Hy draai die bord 500 keer.
  
         8.3.1  Hoeveel keer behoort Tom
                   die nommer 3 te sien as die
                   bord gebalanseerd is?
                                                           [ A 8.3.1 ]
  
         8.3.2  Tom vind dat nommer 2
                   130 keer voorkom.
                   Bereken die waarskynlikheid
                   dat nommer 2 sal voorkom.
                                                           [ A 8.3.2 ]
  
         8.3.3  Tom vind dat P(1) = 0,15 en
                   P(3) = 0,24. Bereken P(4).
                                                           [ A 8.3.3 ]
  
         8.3.4  Kan jy aflei dat die draaibord
                   ongebalanseerd of sydig is?
                   Verduidelik.                     [ A 8.3.4 ]
  
         8.1  What is the probability that the
                spinner will land on the side
                marked "3"?
                                                           [ A 8.1 ]
  
         8.2  P(1) = P(2) = P(3) = P(4).
                Is this statement correct?
                Explain.
                                                           [ A 8.2 ]
  
         8.3  Tom thinks that the spinner is
                unbalanced. He spins it 500 times.
  
  
         8.3.1  How many times should the
                   number 3 appear if the spinner is
                   balanced?
                                                        [ A 8.3.1 ]
  
         8.3.2  Tom finds that number 2 appears
                   130 times. Calculate the probability
                   that number 2 will appear.
                                                        [ A 8.3.2 ]
  
  
         8.3.3  Tom finds that P(1) = 0,15 and
                   P(3) = 0,24. Calculate P(4).
                                                        [ A 8.3.3 ]
  
         8.3.4  Can you deduce that the spinner
                   is unbalanced? Explain.
                                                        [ A 8.3.4 ]
  
Vraag  / Question  9  
  
         Die tabel hieronder toon die resultate
         van 'n opname wat in 'n Graad 12
         klas gemaak is om vas te stel wat
         die leerlinge per dag by die skool
         se snoepie koop.
         The table below shows the result of a
         survey that was made in a Grade 12
         class to ascertain what the pupils buy
         from the school's tuck shop on a
         daily basis.
  
  
  
  
Seuns / Boys
  
Dogters / Girls
  
Smulstafie / Munch bar
  
2
  
4
  
Sjoklade stafie / Chocolate bar
  
4
  
3
  
Droë vrugte / Dried fruit
  
5
  
12
  
Kooklekkers / Boiled sweets
  
3
  
5
  
Koop niks / Does not buy
  
4
  
8
  
  
         9.1  Hoeveel leerlinge is daar in
                die klas?
                                                           [ A 9.1 ]
  
         9.2  Bereken die volgende
                waarskynlikhede en skryf die
                waarskynlikheid as 'n persentasie :
  
         9.2.1  P(seun).                       [ A 9.2.1 ]
  
         9.2.2  P(koop niks nie).
                                                        [ A 9.2.2 ]
  
         9.2.3  P(koop 'n Smulstafie).
                                                        [ A 9.2.3 ]
  
         9.2.4  P(koop kooklekkers).
                                                        [ A 9.2.4 ]
  
         9.2.5  P(dogter en koop Sjokolade stafie).
                                                        [ A 9.2.5 ]
  
         9.2.6  P(dogter en koop droë vrugte).
                                                        [ A 9.2.6 ]
  
         9.2.7  P(seun en koop Smulstafie).
                                                        [ A 9.2.7 ]
  
         9.2.8  P(seun en koop niks).
                                                        [ A 9.2.8 ]
  
         9.3  Daar is 650 leerlinge in die skool.
                Het genoeg leerlinge aan die
                opname deelgeneem sodat
                'n goeie gevolgtrekking gemaak
                kan word? Verduidelik.
                                                           [ A 9.3 ]
  
         9.4  Sê of die volgende bewerings
                waar of vals is.
                Motiveer jou antwoord.
  
         9.4.1  Die waarskynlikheid dat 'n
                   dogter nie iets sal koop nie
                   is kleiner as die van 'n seun.
                                                        [ A 9.4.1 ]
  
         9.4.2  Die waarskynlikheid dat
                   meer as 494 leerlinge iets
                   sal koop, is groot.
                                                        [ A 9.4.2 ]
  
         9.4.3  Dit is meer waarskynlik dat
                   'n seun 'n Sjokolade stafie koop
                   as wat 'n dogter 'n Sjokolade
                   stafie koop.
                                                        [ A 9.4.3 ]
  
         9.4.4  Meer dogters koop Smulstafies
                   as wat seuns droë vrugte koop.
                                                        [ A 9.4.4 ]
  
         9.1  How many students are there in
                the class?
                                                           [ A 9.1 ]
  
         9.2  Determine the following probabilities
                and write the probability as
                a percentage :
   
         9.2.1  P(boy)                            [ A 9.2.1 ]
  
         9.2.2  P(does not buy anything)
                                                        [ A 9.2.2 ]
  
         9.2.3  P(buys a Munch bar)
                                                        [ A 9.2.3 ]
  
         9.2.4  P(buys boiled sweets)
                                                        [ A 9.2.4 ]
  
         9.2.5  P(girl and buys a Chocolate bar)
                                                        [ A 9.2.5 ]
  
         9.2.6  P(girl and buys dried fruit)
                                                        [ A 9.2.6 ]
  
         9.2.7  P(boy and buys a Munch bar)
                                                        [ A 9.2.7 ]
  
         9.2.8  P(boy and buys nothing)
                                                        [ A 9.2.8 ]
  
         9.3  There are 650 pupils in the school.
                Did enough pupils take part in this
                survey to make a certain decision?
                Explain.
                                                           [ A 9.3 ]
  
  
         9.4  Say whether the following
                statements are true or false.
                Give reasons.
  
         9.4.1  The probability that a girl will not
                   buy anything is smaller than
                   that of a boy.
                                                        [ A 9.4.1 ]
  
         9.4.2  The probability that more than
                   494 pupils will buy something,
                   is good.
                                                        [ A 9.4.2 ]
  
         9.4.3  The probability of a boy buying
                   a Cholate Bar is greater than
                   the probability of a girl buying
                   a Chocolate Bar.
                                                        [ A 9.4.3 ]
  
         9.4.4  More girls buy Munch Bars than
                   boys that buy dried fruit.
                                                        [ A 9.4.4 ]
  
  
Vraag  / Question  10  
  
         'n Blik bevat 3 rooi en 2 groen lekkers.
  
         10.1  'n Lekker word willekeurig uit
                  die blik getrek. Wat is die
                  waarskynlikheid dat die lekker
                  'n . . . sal wees?
  
         10.1.1  rooi lekker                 [ A 10.1.1 ]
  
         10.1.2  groen lekker                 [ A 10.1.2 ]
  
  
         10.2  'n Rooi lekker word uit die blik
                  getrek en nie weer terug geplaas
                  nie. Bereken die waarskynlikheid
                  dat die volgende lekker wat getrek
                  word 'n . . . lekker sal wees.
  
         10.2.1  rooi                           [ A 10.2.1 ]
  
         10.2.2  groen                       [ A 10.2.2 ]
  
  
         10.3  Al die lekkers word terug
                  geplaas in die blik.
                  'n Rooi lekker en dan 'n groen
                  lekker word uit die blik getrek en
                  nie weer terug geplaas nie.
                  nie. Bereken die waarskynlikheid
                  dat die volgende lekker wat getrek
                  word 'n . . . lekker sal wees.
  
         10.3.1  rooi                           [ A 10.3.1 ]
  
         10.3.2  groen                       [ A 10.3.2 ]
  
  
         A tin contains 3 red and 2 green sweets.
  
         10.1  A sweet is withdrawn randomly
                  from the tin. What is the probability
                  that this sweet will be a . . . sweet?
  
  
         10.1.1  red                            [ A 10.1.1 ]
  
         10.1.2  green                        [ A 10.1.2 ]
  
  
         10.2  A red sweet is withdrawn from the
                  tin and not replaced. Calculate the
                  probability that the next sweet
                  withdrawn will be a . . . sweet?
  
  
         10.2.1  red                            [ A 10.2.1 ]
  
         10.2.2  green                        [ A 10.2.2 ]
  
  
         10.3  All the sweets are now replaced
                  in the tin.
                  A red sweet and then a green
                  sweet are withdrawn from the tin
                  and not replaced.
                  Calculate the probability that the
                  next sweet withdrawn from the tin
                  will be a . . . sweet?
  
         10.3.1  red                            [ A 10.3.1 ]
  
         10.3.2  green                        [ A 10.3.2 ]
  
  
Vraag  / Question  11  
  
         Twee dobbelstene word gerol.
         Wat is die waarskynlikheid om
         twee viere te kry?
         Omdat dit moeilik sal wees om 'n
         boomdiagram te teken, gebruik
         ons liewer 'n tabel om die
         uitkomste aan te teken.
         Die uitkomste word as 'n
         dubbel-syfer getal neergeskryf,
         bv. 32 sal 'n 3 op die eerste steen
         en 'n 2 op die tweede steen voorstel.
         Die tabel word hieronder getoon :
  
         Two die are cast. What is the
         probability that two fours will
         be shown?
         Because it it is difficult in this case
         to draw a tree-diagram, we will rather
         use a table to write down all
         the outcomes.
         The outcomes are written down as
         double-digit numbers e.g.
         32 will represent a 3 on the first die
         and a 2 on the second die.
         The table is shown below :
  
  
  
Tweede steen / Second die Eerste steen / First die
  
1
  
2
  
3
  
4
  
5
  
6
  
1
  
11
  
21
  
31
  
41
  
51
  
61
  
2
  
12
  
22
  
32
  
  
  
  
3
  
13
  
23
  
  
  
  
  
4
  
14
  
  
  
44
  
  
  
5
  
15
  
  
  
  
55
  
  
6
  
16
  
  
  
  
  
  
         11.1  Vul die ontbrekende getalle in,
                                                           [ A 11.1 ]
  
           Bereken die waarskynlikheid om
           die volgende te kry
  
         11.2  twee viere
                                                           [ A 11.2 ]
  
         11.3  'n 3 en 'n 4, in enige volgorde
                                                           [ A 11.3 ]
  
         11.4  'n 3 en 'n 4, in daardie volgorde
                                                           [ A 11.4 ]
  
         11.5  twee onewe syfers
                                                           [ A 11.5 ]
  
         11.6  elke syfer kleiner as 3
                                                           [ A 11.6 ]
  
         11.7  elke syfer 'n veelvoud van 3
                                                           [ A 11.7 ]
  
         11.8  die som van die twee
                  syfers is 7
                                                           [ A 11.8 ]
  
         11.9  die som van die twee
                  syfers is groter as 9
                                                           [ A 11.9 ]
  
         11.10  twee gelyke syfers
                                                           [ A 11.10 ]
  
         11.11  die verskil van die twee
                    syfers is kleiner as 3
                                                           [ A 11.11 ]
  
         11.12  die som van die twee syfers
                    is gelyk aan 7
                                                           [ A 11.12 ]
  
         11.13  die som van die twee syfers
                    is kleiner as 13
                                                           [ A 11.13 ]
  
         11.14  die som van die twee syfers
                    is groter as 15
                                                           [ A 11.14 ]
  
         11.15  die produk van die twee syfers
                    is gelyk aan 20
                                                           [ A 11.15 ]
  
         11.16  die produk van die twee syfers
                    is groter as 18
                                                           [ A 11.16 ]
  
         11.17  die produk van die twee syfers
                    is 'n volkome vierkant
                                                           [ A 11.17 ]
  
         11.18  die produk van die twee syfers
                    is 'n veelfout van 8
                                                           [ A 11.18 ]
  
         11.19  die kwosiënt van die twee syfers
                    is 'n natuurlike getal
                                                           [ A 11.19 ]
  
         11.1  Write down the missing values
                                                           [ A 11.1 ]
  
         Calculate the probability to get
         the following
  
         11.2  two fours
                                                           [ A 11.2 ]
  
         11.3  a 3 and a 4, in any order
                                                          [ A 11.3 ]
  
         11.4  a 3 and a 4, in that order
                                                          [ A 11.4 ]
  
         11.5  two uneven digits
                                                          [ A 11.5 ]
  
         11.6  each digit smaller than 3
                                                          [ A 11.6 ]
  
         11.7  each digit a multiple of 3
                                                          [ A 11.7 ]
  
         11.8  the sum of the digits is
                  equal to 7
                                                          [ A 11.8 ]
  
         11.9  the sum of the digits is
                  greater than 9
                                                          [ A 11.9 ]
  
         11.10  two equal digits
                                                          [ A 11.10 ]
  
         11.11  the difference between the digits
                    is smaller than 3
                                                          [ A 11.11 ]
  
         11.12  the sum of the two digits is
                    equal to 7
                                                          [ A 11.12 ]
  
         11.13  the sum of the two digits is
                    smaller than 13
                                                          [ A 11.13 ]
  
         11.14  the sum of the two digits is
                    greater than 15
                                                          [ A 11.14 ]
  
         11.15  the product of the two digits is
                    equal to 20
                                                          [ A 11.15 ]
  
         11.16  the product of the two digits is
                    greater than 18
                                                          [ A 11.13 ]
  
         11.17  the product of the two digits
                    is a perfect square
                                                          [ A 11.17 ]
  
         11.18  the product of the two digits
                    is a multiple of 8
                                                          [ A 11.18 ]
  
         11.19  the quotient of the two digits is
                    a natural number
                                                          [ A 11.19 ]
  
  
Vraag  / Question  12  
  
      'n Span moet nog twee wedstryde speel.
      Die boomdiagram hieronder stel die
      uitkomstes voor.
      
 
 
 
    
    
      12.1   Vul die 3 ontbrekende uitkomstes in.
                                                              Ans. 12.1
    
      Gee die waarskynlikheid, in die
      eenvoudigste vorm, dat
    
      12.2   die span die eerste westryd sal
                verloor                                  Ans. 12.2
    
      12.3   die span die tweede wedstryd sal wen.
                                                              Ans. 12.3
    
      12.4   die span albei wedstryde sal wen.
                                                              Ans. 12.4
    
      12.5   dat die span ten minste een wedstryd
                sal verloor.                            Ans. 12.5
    
      12.6   ten minste een wedstryd gelykop
                sal wees.                              Ans. 12.6
    
      12.7   dat die span nie 'n wedstryd sal
                verloor nie.                           Ans. 12.7
  
      A team still has to pay two matches.
      The tree-diagram below shows all
      the possible outcomes.
      
 
 
 
    
    
      12.1   Write down the 3 missing outcomes.
                                                              Ans. 12.1
    
      Give the probability, in its
      simplest form, that
    
      12.2   the team will lose the first match.
                                                              Ans. 12.2
    
      12.3   the team will win the second match.
                                                              Ans. 12.3
    
      12.4   the team will win both matches.
                                                              Ans. 12.4
    
      12.5   the team will lose at least one match
                                                              Ans. 12.5
    
      12.6   at least one match will be drawn.
                                                             Ans. 12.6
    
      12.7   the team will not lose a match.
                                                             Ans. 12.7
  
  
Vraag  / Question  13  
  
      Daar is drie kinders in 'n gesin.
      Die boomdiagram hieronder stel die
      uitkomstes voor.
      
 
 
 
    
    
      13.1   Vul die 3 ontbrekende uitkomstes in.
                                                              Ans. 13.1
    
      Gee die waarskynlikheid, in die
      eenvoudigste vorm, dat
    
      13.2   die eerste kind 'n seun sal wees.
                                                             Ans. 13.2
    
      13.3   daar twee dogters in die gesin sal
                wees.                                   Ans. 13.3
    
      13.4   daar net een seun in die gesin sal
                wees.                                   Ans. 13.4
    
      13.5   daar geen dogters in die gesin sal
                wees nie.                             Ans. 13.5
  
      There are three children in a family.
      The tree-diagram below represents
      the outcomes.
      
 
 
 
    
    
      13.1   Write down the three missing
                outcomes.                              Ans. 13.1
    
      Write down the probability, in it's
      simplest form, that
    
      13.2   the first child will be a boy.
                                                             Ans. 13.2
    
      13.3   the family will have two daughters.
                                                             Ans. 13.3
    
      13.4   there will be only one boy in the
                family.                                   Ans. 13.4
    
      13.5   there will be no daughters in the
                family.                                   Ans. 13.5
  
  
Vraag  / Question  14  
  
 
 
 
      'n Dobbelsteen word gerol en 'n muntstuk
      word gelyktydig geskiet.
      Die boomdiagram hierbo stel die
      uitkomstes voor.
    
      14.1   Vul die 4 ontbrekende uitkomstes in.
                                                              Ans. 14.1
    
      Gee die waarskynlikheid, in die
      eenvoudigste vorm, dat
    
      14.2   1 en'n kruis verkry word.
                                                             Ans. 14.2
    
      14.3   'n ewe getal en 'n kruis verkry
                word.                                   Ans. 14.3
    
      14.4   'n getal groter as 3 en 'n munt verkry
                word.                                   Ans. 14.4
    
      14.5   'n onewe getal kleiner as 5 en
                munt verkry word.               Ans. 14.5
    
      14.6   enige getal en munt verkry word.
                                                           Ans. 14.6
    
      14.7   3 en kruis of munt verkry word.
                                                           Ans. 14.7
    
      14.8   2 en nie kruis of munt verkry word nie.
                                                           Ans. 14.8
  
      As a die is cast, a coin is tossed.
      The tree-diagram above represents
      all the possible oucomes.
      
    
      14.1   Write down the 4 missing outcomes.
                                                              Ans. 14.1
    
      Write down, in its simplest form, the
      probability that
    
      14.2   1 and a head are obtained.
                                                             Ans. 14.2
    
      14.3   an even number and a head are
                obtained.                              Ans. 14.3
    
      14.4   a number greater than 3 and a tail
                are obtained.                        Ans. 14.4
    
      14.5   an uneven number smaller than 5 and
                a tail are obtained.               Ans. 14.5
    
      14.6   any number and a tail are obtained.
                                                             Ans. 14.6
    
      14.7   3 and heads or tail are obtained.
                                                             Ans. 14.7
    
      14.8   2 and neither heads or tails are obtained.
                                                             Ans. 14.8
  
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