QUESTION 10 Refer to the following payoff table: Alternative A1 A2 Prior Probabi

Question

QUESTION 10 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 state of nature is SI, the research 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. Given that the research is done, what is the joint probability that the state of nature is S1 and the research predicts S27 O A. 0.08 O B. 0.16 OC. 0.24 D. 0.36

Explanation / Answer

Joint probability (State of nature is S1 but research preditcts S2) = Prior probability of S2 * probability of non accurate

= 0.4 * 0.2 = 0.08

Hence, Option (A) 0.08 is the correct choice.

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