The three states are not equiprobable. Suppose that she must say instead which particular state she is most likely to be in: M+T, T+T, or M+H. Well, we know tha

The three states are not equiprobable. Suppose that she must say instead which particular state she is most likely to be in: M+T, T+T, or M+H. Well, we know that Heads is chosen 1/2 of the time, so she should choose M+H! After all, the probability she is in M+T is only 1/4, and the probability she is in T+T is only 1/4. (Since Tails is chosen 1/2 of the time.)