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: Markov chain solution - 2nd part by Charlie)

I disagree: P(i,HHH) and P(i,TTT) should both approach 50% since the problem is completely symmetric. The odds of ending when 3 consecutive heads appear are the same as ending with 3 consecutive tails. The table you provided shows exactly this behavior.

Another point, on notation: when you got 3 H's you stay in that state and you cannot go on to get 3 T's -- in Markov chains terms, HHH and TTT are "final states" or "absorbing states".

Posted by Oskar on 2004-06-13 10:24:11