65 of a colleges faculty have phD 10 of those with their phD

65% of a colleges faculty have phD. 10% of those with their phD are tenured. 15% of the faculty are tenured. What is the probability a tenured faculty member has phD? b) What proportion of tenured faculty do not have their phD?, c) What is the probability a non tenured faculty member has their phD? d) What proportion of non tenured faculty do not have their phD?

Solution

Let

P = has PhD
T = tenured

Thus,

a)

P(P|T) = P(P) P(T|P) / P(T) = 0.65*0.10/0.15 = 0.433333333 [ANSWER]

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b)

P(P\'|T) = 1 - P(P|T) = 1 - 0.433333333 = 0.566666667 [ANSWER]

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c)

P(P|T\') = P(P) P(T\'|P) / P(T\') = 0.65*(1-0.10)/(1-0.15) = 0.688235294 [ANSWER]

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d)

P(P\'|T\') = 1 - P(P|T\') = 1 - 0.688235294 = 0.311764706 [ANSWER]