A person holds a two-tailed coin in one hand and a fair coin in the other. a hand is chosen at random and the coin is flipped. if tails shows, what is the probability that it is the two tailed coin?

Probability that (2 tailed given tail) = probability (tail from 2 tailed) / probability tail probability (tail from 2 tail) = 1/2 * 1 = 0.5 probability tail = tail from 2 tailed + tail from fair coin = 0.5 + 0.5 * 0.5 = 0.75 so final answer = 0.5/0.75 = 0.667