Two fair coins are flipped simultaneously. This is done repeatedly until at least one of the coins comes up heads, at which point the process stops. What is the probability that both coins come up heads?

Question

I think it would be 1/2 but the answer is 1/3 and I have no idea where you would get that answer.

Answer 1

Three things can happen with equal probability on the fateful toss when "at least one" is heads:
Coin A heads; Coin B heads
Coin A heads, Coin B tails
Coin A tails; Coin B heads
That makes one out of three with both heads

Answer 2

Bob flipped a coin 200 times with the following results:120 heads, 80 tails. Based on these results what is the experimental probability that Bob will get a tail on the next flip.

Answer 3

1/2