I have a bag with 3 coins in it. One of them is a fair coin, but the others are biased trick coins. When flipped, the three coins come up heads with probability 0.5, 0.6, 0.1 respectively. Suppose that I pick one of these three coins uniformly at random and flip it three times. (a) What is P(HT T)? (That is, it comes up heads on the first flip and tails on the second and third flips.) (b) Assumimg that the three flips, in order, are HT T, what is the probability that the coin that I picked was the fair coin? (Remember, there is no need to simplify fractions.)

I have a bag with 3 coins in it. One of them is a fair coin, but the others are biased

trick coins. When flipped, the three coins come up heads with probability 0.5, 0.6, 0.1

respectively.

Suppose that I pick one of these three coins uniformly at random and flip it three times.

(a) What is P(HT T)? (That is, it comes up heads on the first flip and tails on the second
and third flips.)
(b) Assumimg that the three flips, in order, are HT T, what is the probability that the coin
that I picked was the fair coin?
(Remember, there is no need to simplify fractions.)