Refer to the following payoff table:   State of Nature Alternative S1 S2 A1 75 −40 A2 0 100 Prior Probability 0.6 0.4 There is an option of paying $100 to have research conducted to better predict which state of nature will occur. When the true state of nature is S1, the research will accurately predict S1 60% of the time. When the true state of nature is S2, the research will accurately predict S2 80% of the time. What is the posterior probability of S1 given that the research predicts S1?   Multiple Choice: 0.18 0.82 0.57 0.44 0.65

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Chapter1: Combinatorial Analysis
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Refer to the following payoff table:

  State of Nature
Alternative S1 S2
A1 75 −40
A2 0 100
Prior Probability 0.6 0.4

There is an option of paying $100 to have research conducted to better predict which state of nature will occur. When the true state of nature is S1, the research will accurately predict S1 60% of the time. When the true state of nature is S2, the research will accurately predict S2 80% of the time.

What is the posterior probability of S1 given that the research predicts S1?

 

Multiple Choice:
  • 0.18
  • 0.82

  • 0.57

  • 0.44

  • 0.65

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