Question

A plane is missing, and it is presumed that it was equally likely to have gone down in any of 3 possible regions. Let 1−βi, i = 1, 2, 3, denote the probability that the plane will be found upon a search of the ith region when the plane is, in fact, in that region.

What is the conditional probability that the plane is in the ith region given that a search of region 1 is unsuccessful?

Suppose βi = ⅓ for i = 1, 2, 3. Interpret the results.

Suppose β1 = 0.2, β2 = 0.3 , β3 = 0.5. Interpret the results.

Suppose β1 = 0.8 , β2 = β3 = 0.1. Interpret the results.

Note that P(R1|E) is always the smallest in the three cases considered. (i) Will this always be the case. Why? Provide a heuristic explanation for why P(R1|E) is always the smallest.

Answer 1