I threw a coin n times, and never got three tails in a row. I calculated the odds of this event, and found out they were just about even; 50%-50%. How many times did I throw the coin?

A second question: what were the chances of having not gotten three heads in a row either?

(In reply to re(2): Markov chain solution - 2nd part by Old Original Oskar!)

Why should they not both approach 100% rather than 50%?  Achieving one does not prevent the other.  If you go long enough, you're overwhelmingly likely to achieve runs of both 3 heads and 3 tails. I agree that they are symmetric, but two 100's are just as symmetric as two 50's. The two final, absorbing states are not mutually exclusive.

Also, your solution for part one correctly stated the probability of having achieved 3 T's in 10 tosses is 50.8%, but in part 2 you say that same probability is 41.3%.

Edited on June 13, 2004, 10:41 am

Posted by Charlie on 2004-06-13 10:32:10