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For years, the manager of a certain company had sole responsibility for making decisions

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For years, the manager of a certain company had sole responsibility for making decisions with regard to company policy. This manager has a history of making the correct decision with a probability of p. Recently company policy has changed, and now all decisions are to 3 be made by majority rule of a three-person committee

a. Each member makes a decision independently, and each has a probability of p of making the correct decision. What is the probability that the committee's majority а. decision will be correct?

b. Ifp 0.1, what is the probability that the committee makes the correct decision?

c. If p 0.8, what is the probability that the committee makes the correct decision?

d. For what values of p is the committee more  likely to make the correct decision by majority rule than the former manager?

e. For what values (there are three) of p is the probability of a correct decision the same for the manager and for the committee? Justify your answer

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[Solved] For years, the manager of a certain company had sole responsibility for making decisions

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