A plane is missing and it is presumed that it was equally likely to have gone down in any of three possible regions. Let 1i

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?