Here is the situation: I have a two-sided, fair coin that I'm going to flip twice in a row. Before starting the experiment, the probability of any possible result of 2 flips (head-head, head-tail, tail-head, tail-tail) is 25% because there is a 50% chance of any given result per flip, twice in a row or 1/2 * 1/2 = 1/4 = 25%
My question is what happens if I evaluate the probability of the second flip, after the first flip has already occurred. In my math class, the teacher answered that the probability of a result on the second flip is still 25%, but this doesn't make sense to me. If the coin is memoryless, why would it not be 50% that say, after having gotten a heads on the first flip, the probability of tails coming up on the second flip would be 50% since past results can't influence future outcomes?