Well the answer of 50% is not just mathematically correct, it's simply correct, because the question said we must assume that the coin is fair. If this was a r

Well the answer of 50% is not just mathematically correct, it's simply correct, because the question said we must assume that the coin is fair. If this was a real life situation, we would assume a reasonable prior for the probability of heads, perhaps with a spike around 0.5 and a small value everywhere else. The posterior would be centered near 1.