a game is played in which a coin is tossed untill the third tail when the game stops, what is the probability that there will be at least three heads before the game stops...?

Question

anonymous · Answer

Each time you toss the coin you have a 1/2 probability it will be heads or tails. The probability of getting two of the same in a row is (1/2)(1/2)=(1/4)
So it depends on how many iterations of throwing the coin were done.

anonymous · Answer

that's the only information given...

barrycarter · Answer

It's tempting to say that the answer is 50% by symmetry, but I don't think that's actually true.

barrycarter · Answer

If the game stops in 6 or more flips, we know that there are 3 tails, 
so the rest must be heads, which means there are at least 3 heads. 
 
If the game stops in 5 or fewer slips, there can be at most 2 heads. 
 
The game can't stop in fewer than 3 flips. 
 
So, you only have to consider the cases of 3, 4, and 5 flips.