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 then 6 P.M. with probability of .8 but if she comes comes home by route B, then she will be home no later then 6 P.M. with a probability of .7. In the past the proportion of times that Amy chose route A is .4.
A. What proportion of times is Amy home no later then 6 P.M. ?
B. IF Amy is home after 6 P.M. today, what is the probability that she took route B?