1. The looks do not have any effect on where the plane is, only on our assessment to the probability that the plane is in each of the possible locations. You may consider the problem embedded within a larger meta-problem where an ensemble of planes crash with the appropriate proportions of cases with the plane in each of the regions.

2. You do not need to worry about the possibility of the plane being elsewhere in this problem, one of the regions may be considered to include the elsewhere if there is such.

3. Let , and denote the prior probabilities that the plane is in regions 1, 2 and 3 respectivly. A look is made in region 1 and the plane not found. Let , and denote the posterior probabilities, then by Bayes theorem:

Also and which will allow the computation of and

CB