Suppose that you have three coins: two fair coins, for which the probability of H is 0.5 and the probability of T is 0.5; and a biased coin, for which the probability of H is 0.8 and the probability of T is 0.2. You choose a coin in such a way that each coin is equally likely to be chosen. You flip the coin three times, getting H all three times. What is the probability that the coin is the biased coin