Question

Suppose a group of research proposals was evaluated by a panel of experts to decide whether or not they were worthy of funding. When these same proposals were submitted to a second independent panel of experts, the decision to fund was reversed in 52 % of the cases. If the probability that a proposal is judged worthy of funding by the first panel is 0.27, what is the probability that a worthy proposal is disapproved by both panels

Answer 1

0.3504 = 35.04% probability that a worthy proposal is disapproved by both panels

Explanation:

We have that:

0.27 = 27% of the time, the proposal is judged worthy of funding by the first panel. So 100 - 27 = 73% probability of being disapproved.

52% of the time, the independent panel reverses the decision. So if the first panel disapproves the funding, 52% probability the second approves the funding and 100 - 52 = 48% probability it does not.

What is the probability that a worthy proposal is disapproved by both panels?

48% of 73%. So

0.48*0.73 = 0.3504

0.3504 = 35.04% probability that a worthy proposal is disapproved by both panels