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 S2?

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The Answer of  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 S2?

There Is an Option of Paying $100 to Have Research