Chris has two commuting routes, A and B, with respective probabilities of arriving home before 6 p.m. being 0.9 and 0.7. He chooses route A 60% of the time. The overall probability of him being home before 6 p.m. is 0.82, and if he is home after 6 p.m., the probability associated with route B being chosen is 0.12.

1. Chris commutes to work on two different routes A and B. If Chris comes home by route A, then
he will be home before 6 P.M. with probability 0.9. If Chris chooses route B, then he will be
home before 6 P.M. with probability 0.7. In the past, the proportion of times that Chris chose
route A is 0.6.
(a) What proportion of times is Chris home from his office before 6 P.M.?
(b) If Chris is home after 6 P.M. today, what
Solution
a)P = (0.6*0.9)+(0.4*0.7) = 0.54+0.28 = 0.82 b)P = 0.4*0.3 = 0.12