There Is an Option of Paying $100 to Have Research

Multiple Choice

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 S1 and the research predicts S1?

A) 0 08
B) 0 16
C) 0 24
D) 0 32
E) 0 36