Iron Bowl At an Auburn–Alabama game, 80 percent of attendees wore Alabama gear and 20 percent wore Auburn gear. During the game, one of the attendees apparently robbed a beer stand outside the stadium. A witness (who was neither an Alabama nor an Auburn fan) later told police that the robber wore Auburn gear. The witness, however, was the beer stand’s best customer, and it was estimated that he would only be able to identify the correct gear about 75 percent of the time. 

What is the probability that the robber wore Auburn gear, given that the witness said that he did? Here is a slightly different kind of problem.