Suppose a group of research proposals was evaluated by a pan

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 30% 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? (Enter your answers to two decimal places.)

A worthy proposal is disapproved by both panels.

A worthy proposal is approved by one panel.

Solution

Probability that a worthy proposal is disapproved by both panels = 0.8*0.3 = 0.24

Probability that a worthy proposal is approved by one panel = 0.2+0.7-0.24 = 0.66