Anna and Bryce are playing a game of coin flips. Anna gets one point for a head, and Bryce gets one for a tail. Whoever secures 10 points win the game. At present, Anna leads 8 – 7. What is the probability that she eventually wins?
The maximum number of games possible from now is four (a best of 19 will lead to 10, and 15 games are over). The simplest solution is to list all the possibilities that favour Anna and estimate the probabilities of those occurrences. They are
| Outcome | Probability |
| HH | 1/4 |
| HTH | 1/8 |
| HTTH | 1/16 |
| THH | 1/8 |
| TTHH | 1/16 |
| THTH | 1/16 |
| Total | 11/16 = 0.6875 |
