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There is an 80% probability the existing cable company will sell if an influential director resigns...

There is an 80% probability the existing cable company will sell if an influential director resigns and a 12% probability the existing cable company will sell if the influential director does NOT resign. The new communications company believes there is a 40% chance the director will resign .Given that the cable company has decided to sell, what is the probability the influential director resigned?

math   Statistics-And-Probability   
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Answer #1

Bayes' Theorem: P(A | B) = P(A & B) / P(B)

P(influential director resigned) = 0.40

P(influential director did not resign) = 0.6

P(cable company has decided to sell) = 0.4x0.80 + 0.6x0.12

= 0.3920

P(influential director resigned | cable company has decided to sell) = P(influential director resigned and cable company has decided to sell) / P(cable company has decided to sell)

= 0.4x0.8/0.3920

= 0.8163

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