6.1 Being discrete

Sometimes it seems like probability is the study of flipping coins or rolling dice, given the number of books that explain it those ways. It’s very hard to break away from these convenient examples. An advantage shared by both of them is that they make it is easy to explain discrete events and independence.

For the sake of mixing it up, suppose we have a cookie machine. It’s a big box with a button on top. Every time you press the button, a cookie pops out of a slot on the bottom. There are four kinds of cookies: chocolate, sugar, oatmeal, and coconut.

Assume for the moment there is no limit to the number of cookies our machine can distribute. If you hit the button a million times, you get a million cookies. Also assume you get a random cookie each time. What does this mean, ‘‘random’’?

Without a rigorous definition, random here means that the odds of getting any one of the cookies is the same as getting...