Question

Teachers and college degrees Select an adult at random. Define events D: person has earned a college degree, and T: person’s career is teaching. Rank the following probabilities from smallest to largest. Justify your answer.

$P\left(D\right)P\left(T\right)P\left(\frac{D}{T}\right)P\left(\frac{T}{D}\right)$

Short answer

The order is$P(\mathrm{T})<P(\mathrm{T}\mid \mathrm{D})<P\left(\mathrm{D}\right)<P(\mathrm{D}\mid \mathrm{T})$

Step-by-step solution

Given Information

It is given that

D: Person earned college degree

T: Person's career is teaching

$P\left(\mathrm{D}\right)$Probability of person earning a college degree

$P\left(T\right)$ Probability for professional teacher

$P(\mathrm{T}\mid \mathrm{D})$ Conditional probability for degree holder professional teacher

$P(\mathrm{D}\mid \mathrm{T})$ Conditional probability for teaching career degree holder

Explanation

All teachers have college degree as per universal fact.

• $P(\mathrm{D}\mid \mathrm{T})$is largest as lot of people have college degree.
• $P\left(\mathrm{D}\right)$ is next largest as most degree holders are not having teaching career.
• $P(\mathrm{T}\mid \mathrm{D})<P\left(\mathrm{D}\right)$ as the professional teachers are less than the people with a college degree opting for teaching career.
• Also $P(\mathrm{T}\mid \mathrm{D})>P\left(T\right)$

The order is$P(\mathrm{T})<P(\mathrm{T}\mid \mathrm{D})<P\left(\mathrm{D}\right)<P(\mathrm{D}\mid \mathrm{T})$