In: Statistics and Probability
A plane is missing, and it is presumed that it was equally
likely to have gone down
in any of 4 possible regions. Let 1 βi, i = 1, 2, 3, 4, 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. (The constants βi 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 1st region
given that a search of region 1 is
unsuccessful?