Chapter 5.3, Problem 68E

To determine

Probabilities are to be ranked in ascending order.

Answer to Problem 68E

From smallest to largest,

  $P\left(\text{T}\right)<P\left(\text{T}|\text{D}\right)<P\left(\text{D}\right)<P\left(\text{D}|\text{T}\right)$

Explanation of Solution

Given information:

Events:

D: Person has earned a college degree

T: Person’s career is teaching

Probabilities:

  $P\left(\text{D}\right)$ : Probability for person earned a college degree

  $P\left(\text{T}\right)$ : Probability for professional teacher

  $P\left(\text{T}|\text{D}\right)$ : Conditional probability for degree holder professional teacher

  $P\left(\text{D}|\text{T}\right)$ : Conditional probability for teaching career degree holder

According to the universal fact,

All teachers have college degree.

Thus,

  $P\left(\text{D}|\text{T}\right)$ will be the largest probability.

Since, there are a lot of people having college degree.

Thus,

  $P\left(\text{D}\right)$ should be the next largest probability.

Since, most degree holders do not have teaching career.

Thus,

  $P\left(\text{T}|\text{D}\right)$ is smaller than $P\left(\text{D}\right)$ .

Since, the professional teachers are less than the people with a college degree opting for teaching career.

Thus,

  $P\left(\text{T}|\text{D}\right)$ is larger than $P\left(\text{T}\right)$ .

Thereby,

Arranging the probabilities from smallest to largest:

  $P\left(\text{T}\right)<P\left(\text{T}|\text{D}\right)<P\left(\text{D}\right)<P\left(\text{D}|\text{T}\right)$