MATHEMATICS
MORE EXERCISES
Probability - tree diagrams.

Question  1
A metal disc has a white and a red surface.
It is tossed thrice.
1.1  Draw a tree diagram to show all
the possible outcomes.                              [ A 1.1 ]

1.2  Use the diagram to calculate the
following probabilities. in simplified
fraction form :
1.2.1  P(three white)                                       [ A 1.2.1 ]

1.2.2  P(only one white)                                 [ A 1.2.2 ]

1.2.3  P(at least one red)                                [ A 1.2.3 ]

1.2.4  P(two or more white)                          [ A 1.2.4 ]

Question  2
Three cards are withdrawn from a pack of
52 playing cards, without replacing the cards.
The colour of the card, black, S, or red, R, is noted.

2.1  Draw a tree diagram to show all
the possible outcomes.                              [ A 2.1 ]

2.2  Use the diagram to calculate the
following probabilities. in simplified
fraction form :

2.2.1  P(two black and one red)                    [ A 2.2.1 ]

2.2.2  P(no red cards)                                      [ A 2.2.2 ]

2.2.3  P(2 black and 1 red, in that order)
[ A 2.2.3 ]

2.2.4  P(two or more red)                               [ A 2.2.4 ]

Question  3
A bag contains 10 coins, x R1 coins, 3 R2 coins
and 2 R5 coins. Two coins are now withdrawn
from the bag without replacing them.

3.1  Determine x if the probability of
witdrawing a R1 coin is 0.5                   [ A 3.1 ]

3.2  Draw a tree diagram to show all
the possible outcomes.                          [ A 3.2 ]

3.3  Now use your diagram to calculate
the probability, in simples fraction form,
that the coins withdrawn are
3.3,1  two R5 coins                                         [ A 3.3.1 ]

3.3,2  a R2 coin and a R1 coin.                     [ A 3.3.2 ]

3.3,3  a R2 coin and a R5 coin, in that
order.                                                      [ A 3.3.3 ]

3.3,4  a R1 coin and a R5 coin.                     [ A 3.3.4 ]

Question  4
Harry shoots arrows at a target board.
He has a 50% chance of hitting the
bull's eye on each shot.

4.1  Calculate the probability that Harry
will hit the bull's eye in his first shot
and his second shot. (2)                           [ A 4.1 ]

4.2  Calculate the probability that Harry
will hit the bull's eye at least twice
in his first three shots. (3)                      [ A 4.2 ]

{ DBE Mathematics Grade 11 Paper 1 November 2020 ]

Question  5
The probability that the first answer in a
maths quiz competion will be correct
is 0,4. If the first answer is correct, the
probability of getting the next answer
correct rises to 0,5. However, if the first
answer is wrong, the probability of getting
the next answer correct is only 0,3.

5.1  Represent the information on a
tree diagram. Show the probabilities
associated with each branch as well as
the possible outcomes.    (3)                   [ A 5.1 ]

5.2  Calculate the probability of getting
5.2.1  the second answer correct.    (3)       [ A 5.2.1 ]
5.2.2  one answer correct and the other
wrong, in that order.                            [ A 5.2.2 ]
5.2.3  at least one answer correct.               [ A 5.2.3 ]

[ DBE Mathematics CAPS-Grade 11 Paper 1 November 2016 ]

Question  6
A group of 200 tourists visited the same
restaurant on two consecutive evenings.
On both evenings, the tourists could either
choose beef (B) or chicken (C) for their
main meal. The manager observed that
35% of the tourists chose beef on the
first evening and 70% of them chose
chicken on the second evening.

6.1  Draw a tree diagram to represent the
different choises of main meals made
on the two evenings. Show on your
diagram the probabilities assosiated with
each branch as well as the possible outcomes
of the choises.    (4)                                    [ A 6.1 ]

6.2  Calculate the number of tourists who
chose the same main meal on both evenings.
[ A 6.2 ]
6.3  Show that more tourists opted not to
change their chose the same main meal
on both evenings.    (2)                             [ A 6.3 ]
[ DBE Mathematics CAPS-Grade 11 Paper 1 November 2019 ]