Originally Posted by

**downthesun01** Honestly, I'm not even sure at this point. On the one hand I would say it's 1/2 because the second flip has no influence on the first flip. But on the other hand, 1/4 seems more likely because E = {HH, HT, TH, TT} and if the second flip has already been determined to be heads, then the only way the first flip can be heads is if the total outcome was {HH}

As you can see, I'm really, really confusing myself with this. 1/4 makes the most sense to me, but I can't see to prove it mathematically.

Edit: Wait, I think I just get it. After looking at what I just typed, the answer does seem to be 1/2 because once it's established that the second flip is heads events {HT} and {TT} get removed since the second flip is tails in both of those, leaving only events {HH} and{TH} as possible outcomes. With these as the only two possible outcomes, it's obvious that the first flip has a 1/2 chance of hitting heads. Is this correct?