Refer to the following payoff table: State of Nature Alternative $2 A1 75 -40 A2 0 100 Prior Probability 0.6 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 S1, the ces research will accurately predict S1 60% of the time. When the true state of nature is $2, the research will accurately predict S2 80% of the time. What is the posterior probability of $2 given that the research predicts S2