I toss a fair coin until I get two head in a row. What is the probability that I toss the coin 5 times in total?
In order to satisfy the condition, must have the 4th toss and 5th toss both being heads. Note that the 3rd toss must be tails as otherwise we would terminate the coin tosses prematurely. This leaves the first two tosses being anything it likes apart from two heads. In total, since probability of the nth toss is independent of other tosses, must have the answer to be 3/4 x (1/2)^3 = 3/16.
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