Lottery Odds (in the wild)

I’m teaching my first class this fall, and I’ve been preparing my notes for class this past week. I wanted to use keno as an example of how to compute probabilities. So I was computing some probabilities and checking them against the posted “odds” on masslottery.com. I couldn’t get my computed odds to match with what the lottery had posted, which led to a brief period of panic that I wasn’t qualified to be teaching this class. Turns out, I’m not computing anything wrong. It’s just that what the lottery is calling “odds” are actually probabilities. Take a look again at masslottery.com and look at the posted odds for a one spot game. For the one spot game they say that the odds are 1:4. This is incorrect. The probability of winning this one spot game is \frac{1}{4}=.25, which would make the odds of winning \frac{.25}{.75}=1:3. Likewise, the odds against winning are 3:1. Generally, if the probability of an event is p, the odds of this even occuring are \frac{p}{(1-p)}.

So what the lottery is referring to as odds are actually probabilities of winning. They actually get this correct that the bottom where they say “Probability of winning a prize in this game = 1:4.00”. The mistake is that they aren’t making any distinction between the probability of winning and the odds of winning when, in fact, these are different.

Cheers.

Posted on August 16, 2010, in Uncategorized. Bookmark the permalink. Leave a comment.

Leave a Reply

Loading cart ...
%d bloggers like this: