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?

Now you'll have to treat HH, HT and TH separately.
P(n+1)=P(n)*(1/2 + 1/4*1/2 + 1/4*1/2)=P(n)* 3/4.
Therefore,
P(n)=3/4 *(3/4)^(n-3)=(3/4)^(n-2).
P(n)=50% -> n=4.4

Posted by Ruopeng Wang on 2004-06-16 11:11:29