EXAMPLE 4.23 Professional Athletes' Pasts

What proportion of professional athletes competed in college? In the notation of Examples 4.21 and 4.22, this is the conditional probability . Before we compute this probability, let's take stock of a few facts. First, the multiplication rule tells us

We know the probabilities and that a high school baseball player does and does not compete in college. We also know the conditional probabilities and that a player from each group reaches MLB. Example 4.22 shows how to use this information to calculate . The method can be summarized in a single expression that adds the probabilities of the two paths to in the tree diagram:

Combining these facts, we can now make the following computation:

About 77% of MLB players competed in college.