(Simple?) probability question...

Three coins. One is fair; one is two-headed; one is two-tailed.

We pick a coin at random, flip it, and it comes out heads. The probability that this coin is the fair one is 1/2.

True or false?
False. Draw a tree. let A be the (HT) coin, B the (HH) and C the (TT). When you make a tree of all possible outcomes, you can easily find


Thanks, John. How about this:

Random variable T = M/(N/x)^1/2 has a t-distribution with x degrees of freedom when N has a chi-squared distribution with x degrees of freedom and M has a normal distribution.
Well, I know that the t-distribution is a ratio of a normally distributed variable divided by an independent chi variable. However, I'm not sure if the degrees of freedom for T would be x just because N has x degrees of freedom...and I'm having trouble finding an answer to that...

Any help would be great.
Yes, I did. I didn't realize it was such a simple conditional probability question at first. I just threw out one more question that's been bugging me. I know it should be in a different forum, so I apologize.