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, 0.3, 0.6 respectively. Suppose that I pick one of these three coins entirely at random and flip it three times.
1. What is P(HTT)? (i.e., it comes up heads on the first flip and tails on the last two flips.)
2.Assuming that the three flips, in order, are HTT, what is the probability that the coin that I picked was the fair coin?
Don't need to reduce fractions
Work:
1. ((.5*.5)/(.5*.5))/3 + ((.3*.5)/(.7*.5))/3+ ((.6*.5)/(.4*.5))/3 - I think this is wrong
2. I dont know how to do 

First:
$$\frac13\cdot \frac18+\frac13\cdot 0.3\cdot 0.7^2+\frac13\cdot 0.6\cdot 0.4^2=0.122667.$$
Second:
$$\frac{\frac13\cdot \frac18}{0.122667}=\frac{0.041667}{0.122667}=0.3397.$$
