A plane is missing and it is presumed that it was equally likely to have
gone down in any of three possible regions. Let 1 − αi denote the probability the plane
will be found upon a search of the ith region when the plane is, in fact, in that region,
i = 1, 2, 3. (The constants αi are called overlook probabilities because they represent the
probability of overlooking the plane; they are generally attributable to the geographical
and environmental conditions of the regions.) What is the conditional probability that the
plane is in the ith region, given that a search of region 1 is unsuccessful, i = 1, 2, 3?