A cute probability problem
I’ve got a lot to do today, so I’ll restrict myself to a very quick post in the series marked Cute Problems. This one is to do with probability.
Two people (A and B) play a game which involves a sequence of tosses of a coin. The coin is “fair” so that the probability of a Head (H) is 0.5, equal to the probability of a Tail (T). Successive tosses of the coin are independent.
The game ends when two successive tosses show either the sequence HT (in which case Player A wins) or the sequence TT (in which case Player B wins). If neither pairing is seen the coin is tossed again and again until either HT or TT is seen.
What is the probability that Player A wins?
Answers (with explanations please) through the comments box..Follow @telescoper