Speaking of sports, newspapers, magazines, and websites often give probabilities as betting odds in the form “Y to Z.” This form means that a bet of $Z will pay you $Y if the team wins. If this is a fair bet, you expect that in the long run you should break even, winning as much money as you lose. In particular, if you bet Y + Z times, on average you should win $Y Z times and lose $Z the other Y times. Thus, on average, if you bet Y + Z times, you win Z of those bets. Odds of Y to Z therefore represent a probability of Z/(Y + Z ) of winning.

On the Web, one can find the current odds of winning the next Super Bowl for each NFL team. We found a list of such odds at www.vegasinsider.com/nfl/odds/futures/. When we checked this website on December 1, 2015, the odds that the New England Patriots would win Super Bowl 50 were 3-to-1. This corresponds to a probability of winning of 1/(3 + 1) = 1/4. The odds that the San Francisco 49ers would with Super Bowl 50 were 6000 to 1. This corresponds to a probability of 1(6000 + 1) = 1/6001.