What is the expected number of times you must toss a (fair) coin until you get n consecutive heads?

Take each group of n flips. There is a 1/(2^n) probability that it is all heads. Therefore, the n heads should start on the (2^n)th flip. The last head will be the ((2^n)+n-1)th flip. Therefore, the answer is (2^n)+n-1.

Posted by Math Man on 2011-04-24 22:27:29