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 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. given that the research is done, what is the joint probability that the state of nature is s2 and the research predicts s1?