Question

Whether a grant proposal is funded quite often depends on the reviewers. Suppose a group of research proposals was evaluated by a group of experts as to whether the proposals were worthy of funding. When these same proposals were submitted to a second independent group or experts, the decision to fund was reversed in 30% of the cases. If the probability that a proposal is approved for funding by the first peer review group is .2, what are the probabilities of these events? (4 points. 1-1/3 point for each part of the question.)

Answer 1

A) 0.14

B) 0.24

C) 0.62

Explanation:

Probability of a worthy proposal being approved by the first review group = P(A) = 0.2

Probability of a worthy proposal NOT being approved by the first review group = P(A') = 1 - 0.2 = 0.8

Probability of a worthy proposal being approved by the second review group = P(B) = P(B|A) = 1 - 0.3 = 0.7 (Since the two events are described as independent events)

Probability of a worthy proposal NOT being approved by the second review group = P(B') = 0.3

A) Worthy Proposal is approved by both groups

Probability = P(A n B) = P(A) × P(B) = 0.2 × 0.7 = 0.14

B) Worthy Proposal is disapproved by both groups

Probability = P(A' n B') = P(A') × P(B') = 0.8 × 0.3 = 0.24

C) Worthy proposal is approved by one group

P(A n B') + P(A' n B) = (0.2×0.3) + (0.8×0.7) = 0.62

Hope this Helps!!!