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A study investigated the effectiveness of Nalmefene (a drug used in the treatment of alcohol dependence)...

A study investigated the effectiveness of Nalmefene (a drug used in the treatment of alcohol dependence) with psychosocial support in decreasing alcohol consumption. Suppose that the probability of a patient to remain in abstinence after a year of treatment( successfully respond) with Nalmefene and psychosocial support is 0.20. The same probability is estimated to be 0.08 if the patient is treated with only psychosocial. Support that you are a physician who have ten new alcoholic patients, and you plan to provide psychosocial support to all of them and also provide treatment with Nalmefene to five of them, Assume that patients respond independently. What is the probability that exactly two of these ten patients successfully responds?

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Answer #1

For first group of 5, P(Recovering) = 0.20

For second group of 5, P(Recovering) = 0.08

Hence,

P(Exactly two out of 10 recovers)

= P(2 from first group) + P(2 from second group) + P(1 from first and 1 from second group)

= 5C2 * (0.20)2 * (1 - 0.20)3 * (1 - 0.08)5 + (1 - 0.20)5 * 5C2 * (0.08)2 * (1 - 0.08)3 + 5C1 * (0.20)1 * (1 - 0.20)4 * 5C1 * (0.08)1 * (1 - 0.08)4

= 0.2687

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