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 6 P.M. with probability 0.8, but if she comes home by route B, then she will be home no later than 6 P.M. with probability 0.7. In the past, the proportion of times that Amy chose route A is 0.4.

(a) What proportion of times is Amy home no later than 6 P.M.?

(b) If Amy is home after 6 P.M. today, what is the probability that she took route \(\mathrm{B}\) ?