Playing around with the odds of winning Powerball

We started chapter 4 in our Introduction to Counting and Probability book today. The topic is combinations. After a few examples and a few problems I introduced them to a “real world” application of this math – lotteries. The specific lottery we looked at was Powerball.

First up, how the game works and what you have to do in order to win the big prize:

After writing down an expression for the odds of winning, we turn to our calculator to see if our expression matches the odds on Powerball’s website. We also spend of time trying to figure out how long you’d have to play before you’d expect to win once:

Finally we explore one of the prizes where the odds look wrong – the odds of matching only the Powerball. Seems like this should be a 1 out of 35 chance, but the website says roughly 1 in 55. Why?

So, a nice – and fairly straightforward – application of permutations and combinations. Definitely a fun way to start off this new chapter.