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

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