Question

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

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

Short answer

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

Step-by-step solution

Step 1. Given Information

$A$: those having a college diploma, and$T$: people who work as teachers.

The probability given are $P\left(A\right)P\left(T\right)P(A/T)P(T/A)$

Step 2. Concept Used

For mutually exclusive events, use the addition rule.

Step 3. Explanation

Because almost all teachers have a college diploma, $P(A/T)$has the highest possibility. $P\left(A\right)$is the second highest probability because there are more persons with a college degree than there are instructors and people with a college degree who become teachers. Because there are fewer teachers than people with a college diploma who become teachers, $P\left(T\right)$ is the second highest probability.

As a result, from least to largest, the order is: $P\left(T\right)<P(T/A)<P\left(A\right)<P(A/T)$