According to a recent survey conducted in large company. 30% of the employees su

Question

According to a recent survey conducted in large company. 30% of the employees support the new strategic plan. The survey also reveals that 82% of the employees who have a Ph.D, supports the new strategic plan. We also know that 28% of the employees have a Ph.D. What is the probability that an employee supports the new strategic plan and has a Ph.D.? (This is a joint probability) Show your work. If an employee supports the new strategic plan, what the probability that he or has a Ph.D.? (This is a conditional probability) Show your work.

Explanation / Answer

Given, P(support new strategy) = 0.30, P(support new strategy | have Ph.D) = 0.82, P(have Ph.D) = 0.28

1) Find P(support new strategy and has Ph.D) = P(support new strategy | have Ph.D)*P(have Ph.D) using condition probability formula.

P(support new strategy and has Ph.D) = 0.82*0.28 = 0.2296

2) Find P(has Ph.D | support new strategy) = P(support new strategy and has Ph.D)/P(support new strategy)

P(has Ph.D | support new strategy) = 0.2296/0.30 = 0.7653

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