The Eastmore Program is a special program to help alcoholics. In the Eastmore Program, an alcoholic lives at home but undergoes a two-phase treatment plan. Phase I is an intensive group-therapy program lasting 10 weeks. Phase II is a long-term counseling program lasting 1 year. Eastmore Programs are located in most major cities, and past data gave the following information based on percentages of success and failure collected over a long period of time: The probability that a client will have a relapse in phase I is 0.24; the probability that a client will have a relapse in phase II is 0.2268. However, if a client did not have a relapse in phase I, then the probability that this client will not have a relapse in phase II is 0.91. If a client did have a relapse in phase I, then the probability that this client will have a relapse in phase II is 0.66. Let A be the event that a client has a relapse in phase I and B be the event that a client has a relapse in phase II. Let C be the event that a client has no relapse in phase I and D be the event that a client has no relapse in phase II. (a) Compute P(A), P(B), P(C), and P(D).
P(A) =
0.24

Correct: Your answer is correct.
P(B) =
0.2268

Correct: Your answer is correct.
P(C) =
0.76

Correct: Your answer is correct.
P(D) =
0.7732

Correct: Your answer is correct.

(b) Compute P(B | A) and P(D | C).
P(B | A) =

Incorrect: Your answer is incorrect.
P(D | C) =

(c) Compute P(A and B) and P(C and D).
P(A and B) =
P(C and D) =

(d) Compute P(A or B).
P(A or B) =

(e) What is the probability that a client will go through both phase I and phase II without a relapse?

(f) What is the probability that a client will have a relapse in both phase I and phase II?

(g) What is the probability that a client will have a relapse in either phase I or phase II?