You are given a fair coin and flip it until you get two heads in a row. What is the probability that this takes 5 tosses?
Note: HT, TH, TT are all good for the first and second tosses. All that matters is that the 3rd is a T and the 4th and 5th toss are both heads.
I got 3/32, but I know that's not right as that's the probability that you know there are exactly five tosses, but this question is asking what is the probability that the consecutive heads happens on the 4th and 5th toss on an arbitrarily long sequence of tosses.