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 40% of the cases. If the probability that a proposal is judged worthy of funding by the first panel is 0.2, what are the probabilities of these events? a. A worthy approval is approved by both panels b. A worthy approval is disapproved by both panels c. A worthy approval is approved by one panel
Accepted Solution
A:
Answer: (a) 0.12 (b) 0.32 (c) 0.56Step-by-step explanation:The sample outcomes are Funded or Unfunded. Total sample space is given by:2²= 4Fund = FUnfunded = UP (F) ist panel = 0.2P (U) ist panel = 0.8P (F) 2nd panel = 0.6P (U) 2nd panel = 0.4TOTAL SAMPLE SPACEIst Panel Second Panel F F F U U F U U(a) Probability of both panel approval = P (FF) = 0.2 x 0.6 = 0.12(b) Probability of approval disapproved by both panels = P (UU) = 0.8 x 0.4 = 0.32(c) Probability of a worthy disapproval by one panel = P(FU) + P(UF) = (0.2 x 0.4) +(0.8 x 0.6) = 0.08 + 0.48 = 0.56