The Eastmore Program is a special program to help alcoholics

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 infor- mation 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 0.27; the prob- ability that a client will have a relapse in phase II is 0.23. 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 0.95. If a client did have a relapse in phase I, then the prob- ability that this client will have a relapse in phase II is 0.70. 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. Compute the following:

(a)     P(A), P(B), P(C), and P(D)

(b)    P(B | A) and P(D | C)

(c)     P(A and B) and P(C and D)

(d)    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?