Chapter 7.3, Problem 7.57E

To determine

To find: the following probabilities from smallest to largest and justify the answer.

Answer to Problem 7.57E

  $P\left(T\right)<P\left(T|A\right)<P\left(A\right)<P\left(A|T\right)$

Explanation of Solution

Given:

  $\begin{array}{l}A=\text{person}\text{}\text{has}\text{earned}\text{advanced}\text{degree}\\ \text{T = Person is teaching}\end{array}$

Arbitrary chose an adult, and then most likely to chose a person which has earned an advanced degree than a person who is teaching.

  $P\left(A\right)>P\left(T\right)$

Mainly teachers are having advanced degree and therefore if a person is a teacher, then this person is more likely to have and advanced degree compared to the proportion of people with advanced degrees.

  $P\left(A|T\right)>P\left(T\right)$

It is look forward that people with advanced degrees to be more likely to be teachers than people.

  $P\left(T|A\right)>P\left(T\right)$

The people with advanced degree, in most of them would not be teachers and there would be a very less proportion of the teachers among the people with advanced degrees.

  $P\left(A\right)>P\left(T|A\right)$

Combining all the conditions

  $P\left(T\right)<P\left(T|A\right)<P\left(A\right)<P\left(A|T\right)$

Answer may vary