Chapter 5.3, Problem 73E

To determine

To arrange: the given probabilitiesfrom smallest to largest.

Answer to Problem 73E

  $P\left(B\right)<P\left(B/T\right)<P\left(T\right)<P\left(T/B\right)$

Explanation of Solution

Given:

Events T: person is over 6 feet tall, and B person is a professional basketball player.

The given probabilities are $P\left(T\right)P\left(B\right)P\left(T/B\right)P\left(B/T\right)$ .

Calculation:

A known fact is that most basketball players are very tall and thus $P\left(T/B\right)$ is the largest probability.

There are a lot of tall people and thus the next largest probability should be $P\left(T\right)$ .

Most tall people do not play basketball, thus $P\left(B/T\right)$ is smaller than $P\left(T\right)$ , but larger than $P\left(B\right)$ since tall people are most likely to play bassket ball.

Thus, the arrangement from smallest to largest is:

  $P\left(B\right)<P\left(B/T\right)<P\left(T\right)<P\left(T/B\right)$