Here’s a question I like to call "Should You Be Happy?"
Here’s how it goes. Naturally, you’re a big fan of the Devereaux University Bear-Riding Clifftop Dynamite Tennis team. They’ve made it to the Championship game, which is a series of thirteen games. Whoever wins the most games wins the championship game. Our team has only a 46% chance of winning each game. Unfortunately, we lost the first two games of the series. In your despair, you tore your clothes, put ashes on your head, and went into isolation for three days. When you return, you find out that we won two games and lost a game. So the series is 2-3. The question is, should you be happy?
On the one hand, you’ve certainly won more games than before. But on the other hand, you’re still behind, and now there are fewer games to make it up. To resolve the issue, examine how the probability of winning now compares to your probability of winning before.