Let F be the hypothesis that the coin is fair, B be the hypothesis that the coin is biased, E be the evidence that the coin just landed on heads, and N be the statement that the coin will land on heads next time. Then the question is asking us to evaluate . We can apply the axioms of probability theory and the definition of conditional probability to show that . See if you can figure out what the expressions P(N|E&F) and P(N|E&B) are. Once you do, the only thing remaining is to figure out P(F|E) and P(B|E).

To do this, apply Bayes' theorem. Bayes' theorem tells us that Figure out what to plug in for each of the probabilities.