Question: please help me solve this and the steps to vet to the answer Refer to the following payoff table: There is an option of paying

please help me solve this and the steps to vet to the answer

Refer to the following payoff table: 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 S160% of the time. When the true state of nature is S2, the research will accurately predict S280% 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 $1

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