Hmm, a bit more involved maybe, but not that much. But your calculation sure seems short. With S = sleeper, and L = letter L, and remembering "total probabilit

Hmm, a bit more involved maybe, but not that much. But your calculation sure seems short. With S = sleeper, and L = letter L, and remembering "total probability": P(L) = P(L|S)P(S) + P(L|-S)P(-S), (where -S is not S), we have by Bayes P(S|L) = P(L|S) P(S) / P(L) = P(L|S) P(S) / (P(L|S)P(S) + P(L|-S)P(-S)) = 1/6 * 1/5 / (1/6*1/5 + 1/4*4/5) = 1/30 / (1/30 + 6/30) = 1/7