Question

Amy commutes to work by two different routes A and B. If she comes home by route A then she will be home no later than 6pm. with probability 0.8, but if she comes home by route B, then she will be home no later than 6pm. with probability 0.7. In the past, the proportion of time that Amy chose route A is 0.4.
a. What proportion of times is Amy home no later than 6pm.?
b. If Amy is home after 6pm. today, what is the probability that she took route B?

Answer 1

The probability problem above can be represented in tree diagram as shown below

Question a)
Probability of Amy gets home before 6 pm is $0.4$×$0.8=0.32$

Question b)
Probability of Amy gets home after 6 pm GIVEN that she took route B is
P(getting home after 6 pm)/P(Route$\frac{0.08*0.18}{0.6} =0.43$ B)