Quote:
Originally Posted by heehaww
12.5% already is for a specific side: each H is 1/2 so P(HHH)=1/8
P(HHH or TTT) = 25%
I think it may help the OP to expand upon this a little more to show the incorrect reasoning that led the OP to say the probability of flipping three simultaneously and having all be the same is 1/8.
Let's say you flip 1 coin (Coin A) and don't look at the result (you hide it under a cup or something). Then the question becomes what is the probability that when you flip the next two coins that they will match Coin A? It is 1/2 * 1/2, no matter what is under the cup.
Put another way, by saying it's 1/2 * 1/2 * 1/2 you've already decided that Coin A has to be a specific thing to meet the success condition because the probability that Coin A is going to be H
or T is 1, not 1/2 (neglecting it landing on its edge or any physical processes that would cause the coin to disintegrate). So it's expressed as 1 * 1/2 * 1/2.