Dear Uncle Colin,

I’m told that two teams play a five-game series. The first team wins the series, but the second team wins the second game. What’s the probability that the second team also won the first game? (Assume that the probability of winning each match is 50% and the matches are independent.)

Mulling A Tournament’s Combinarical Hurdles

Hi, MATCH, and thanks for your message!

I would imagine there are many ways to approach this, but I’m going to go at it sledgehammer fashion.

If we know that the second team (let’s call them B) won the second match, we can just ignore that game and consider the remaining four, of which the first team (A) won at least three.

Either team A won all four of the remaining games (one way), or they won three and B won one (four ways).

There are five possibilities, and B won the first game in only one of them – so the probability is 1/5.

Hope that helps!

- Uncle Colin