48. A high school student is anxiously waiting to receive mail telling her whether she has been accepted to a certain college. She estimates that the conditional probabilities, given that she is accepted and that she is rejected, of receiving notification on each day of next week are as follows:

Day | P(mail accepted) | P(mail rejected)

------- | -------- | --------

Monday | .15 | .05 Tuesday | .20 | .10 Wednesday | .25 | .10 Thursday | .15 | .15 Friday | .10 | .20 She estimates that her probability of being accepted is .6.

(a) What is the probability that mail is received on Monday?

(b) What is the conditional probability that mail is received on Tuesday given that it is not received on Monday?

(c) If there is no mail through Wednesday, what is the conditional probability that she will be accepted?

(d) What is the conditional probability that she will be accepted if mail comes on Thursday?

(e) What is the conditional probability that she will be accepted if no mail arrives that week?