M-35
Probability 3 : Tree Diagrams
Answer on this sheet
1. The probability of a day being windy is 0.6. If it’s windy the
probability of rain is 0.4. If it’s not windy probability of rain
is 0.2.
rainy
windy
(a) Complete the tree diagram on the right.
not rainy
(b) What is the probability of a given day being rainy?
rainy
(c) What is the probability of two successive days not being
rainy?
not windy
not rainy
2. In a bag are 4 red balls, 3 green balls and 2 yellow
balls. A ball is chosen at random, and not replaced.
A second ball is then chosen.
(a) In the tree diagram, explain the entry
R
R
Y
3
.
8
R
G
(b) Complete the tree diagram.
(e) Find p(at least one ball is yellow)
G
Y
(c) Find p(the balls are both green)
(d) Find p(the balls are the same colour)
G
R
Y
G
Y
(f) Find p(neither ball is red)
3. On any given day there’s a 0.8 probability that I’ll be happy. If I’m happy there’s a 0.7 probability I’ll study
hard for the test, but if I’m not happy there’s only a 0.2 probability.
(a) Construct a tree diagram and find the probabilities that (i) I study hard, and (ii) I don’t study hard.
(b) If I study hard for the test there’s a 0.6 probability that I’ll get a good grade, but if I don’t study hard
there’s only a 0.2 probability. Using a tree diagram or otherwise find the probability that I get a good grade.