I am preparing for my probability class next semester. There is a question on Bayes Theorem that I can't seem to understand.
A box has N coins such that X of these coins have two heads, Y have one head and one tail, and N = X + Y. A coin is randomly chosen and flipped, and it comes up heads. What is the probability that the selected coin has one head and one tail.
My attempt is, of course, to use Bayes theorem based on this example. However, there are X and Y coins, instead of 2 coins as in the example. How can I determine a probability of head? Would it be $$\left(\frac{1}{2}\right)^Y$$ for the fair coin, and $$1^X$$ for double headed coin?
Any help or suggestion is appreciated. Thanks all!