In assessing the effecitveness of a new treatment: 70% of all participants enter

Question

In assessing the effecitveness of a new treatment: 70% of all participants entering the study will never successfully get positive results. Among the remaining individuals who could potentially get positive results: there is a 50% probability of success on any given attempt, independent of the results of any previous attempts.

What fraction of all participants in the study will success on the first attempt?

What fraction of participants who fail to success on the first attempt and who make a second attempt will success on the second attempt?

Explanation / Answer

P(P) = 0.3, P(P') = 0.7
P(S|P) = 0.3*0.5 = 0.15

What fraction of all participants in the study will success on the first attempt?
P(S|P) = 0.3*0.5 = 0.15

What fraction of participants who fail to success on the first attempt and who make a second attempt will success on the second attempt?
Required probability = P(S'|P)*P(S|P)
= (1-0.15)*0.15 = 0.1275

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