6 . a. ) Approved first peer review = 0.2 Approved second review = not reversed = 1-0.3=0.7 ( 0 . 7) (0.2 ) = 0.14 b. ) Disapproved first peer review = not approved first review = 1 - 0.2 = 0.8 Original decision not reversed second review = 1-0.3 = 0.7 ( 0.8 ) (0.7 ) = 0.56 C. ) P (A ) = funded the first time = 0.2 D (A) = not funded the first time = 0.8 P (B) = reversed clecision = 0.3 P ( BA) = upheld / stays the same = 0.7 Ist way : funded first time, reversed / rejected second time - P(A) * PCB) -(0. 2) (0.3) = 0.06 2 nd way : rejected first time, reversed & approved second time - P(AP) * D (B ) - (0 .8 ) ( 0 . 3 ) = 0.24 Total for both outcomes = 0-06 +0. 24 = 0.36 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.) A. Proposal is approved by both groups B. Proposal disapproved by both groups C. Proposal is approved by only one group