Question

Probability and Stats: 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 reverse in 74 % of the cases. If the probability that a proposal is judged worth of funding by the first panel is 22 %, what is the probability that a worthy proposal is disapproved by both panels?

Answer 1

Answer: Let's define the events:

A: a proposal is judged worthy of funding by the first panel

B: the decision to fund a proposal is reversed by the second panel

We want to find the probability of the intersection of events A and B (i.e., a worthy proposal is disapproved by both panels). We can use the formula:

P(A and B) = P(B|A) * P(A)

We know that P(A) = 0.22 (the probability that a proposal is judged worthy of funding by the first panel). We also know that when a proposal is judged worthy of funding by the first panel, the probability that the decision to fund is reversed by the second panel is 0.74 (i.e., P(B|A) = 0.74).

Plugging in these values, we get:

P(A and B) = 0.74 * 0.22 = 0.1628

Therefore, the probability that a worthy proposal is disapproved by both panels is 0.1628, or approximately 16.28%.

Explanation: