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 in those ways. It’s tough to break away from these convenient examples. An advantage shared by both is that they make it easy to explain discrete events and independence. A set of events is discrete if there are only a finite number of them or if we can put them in one-to-one correspondence with Z. sample space$discrete

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. You get a million cookies if you hit the button a million times. Also, assume you get a random cookie each time. What does this mean, “random...