Question

A hiker has gone missing. The hiker took one of three trails: A, B, or C. Due to the popularity of the trails, it is assumed that the (prior) probabilities of the hiker taking these trails are 0.4 (A), 0.1 (B), and 0.5 (C). Each trail has a different terrain, so the probability of successfully finding the hiker, if there, is 0.6 (A), 0.85 (B), and 0.55 (C). Because C is the most commonly hiked trail (even though it is the hardest to search), a search is conducted along trail C. Ultimately, the search turns out to be unsuccessful (either the hiker is not there, or the hiker was well hidden and the search failed).

Given that the search along trail C was unsuccessful, what are the posterior probabilities that the hiker is along trail A? B? C?

Answer 1