Answer using the following table

Alternative State of high nature State of low nature Buy 50 10 Lease 20 100 Prior Probability 0.6 0.4

There is an option of paying $100 to have research conducted to better predict which state of nature will occur. When the true state of nature is high, the research will accurately predict high 70% of the time. When the true state of nature is low, the research will accurately predict low 75% of the time.

Given that the research is conducted, what is the joint probability that the state of nature is high and the research predicts low?

Joint Probability answer to the 2 decimal