A coin flip has a 1/2 chance of being head or tail. It is said that the current flip has no relation to the previous flips and hence the chance remains at 1/2.
However, from what I was taught at school, the chance of getting 2 heads in a row is
1/2 * 1/2 = 1/4. If I go ahead and flip the coin for the third time, the probability of getting a head is now
1/4 * 1/2 = 1/8. Therefore the previous coin flip outcomes do have affect on the future ones.
Is the first claim about independency correct, or the math in the second claim correct? This is probably basic math but I cannot seem to find the answer anywhere or what to search for.