Refer to the following payoff table (values are profit): State of Nature Alternative 51 52 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 51. the research will accurately "predict S1" 60% of the time. When the true state of nature is 52, the research will accurately "predict 52" 80% of the time. What is the probability that the research predicts 52 [Le prreclict 52)]? 0.32 0.44 0.56 :::- 0.6