Refer to the following payoff table: Alternative A1 A2 Prior Probability 0.6 Sta

Question

Refer to the following payoff table: Alternative A1 A2 Prior Probability 0.6 State of Nature S1 75 0 S2 -40 100 0.4 There is an option of paying $100 to have research done to better predict which state of nature will occur. When the true stat of nature is si theresearch will accurately predict SI 60% of the time when the true state of nature is S2, the research will accurately predict S2 80% of the time. S17 Given that the research is done, what is the joint probability that the state of nature is S1 and the research predicts OA. 0.08 O B. 0.16 ? C. 0.24 D. 0.36

Explanation / Answer

Joint probability (State of nature is S1 and research predicts S1)

= Probability that research accurately predicts S1 * P (S1) = 0.6 * 0.6 = 0.36

Hence, Option (D) 0.36 is the correct choice.

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