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: solution by Old Original Oskar!)

Ah, yes, rereading the question in the light of your comment, that does seem an appropriate way of interpreting the second question.

The probability of having gotten no three heads in a row given that no three tails were in a row is

P(~3H / ~3T) = P(~3H & ~3T) / P(~3T)

= 0.17383 / 0.49219 = .35318

(about a 35% probability).

Posted by Charlie on 2004-06-12 10:15:33