Question

Tall people and basketball players Select an adult at random. Define events $T$: a person is over $6$ feet tall, and $B$: a person is a professional basketball player. Rank the following probabilities from smallest to largest. Justify your answer.

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

Short answer

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

Step-by-step solution

Step 1. Given Information

Events $T$: individual is over $6$feet tall, and $B$: individual is a professional basketball player. The probability given are $P\left(T\right)P\left(B\right)P(T/B)P(B/T)$

Step 2. Concept Used

For mutually exclusive events, use the addition rule.

Step 3. Explanation

Because most basketball players are extremely tall, $P(T/B)$ has the highest likelihood. Because there are so many tall people, the next highest probability should be$P\left(T\right)$ Because most tall people do not play basketball, $P(B/T)$ is less than $P\left(T\right)$, but larger than $P\left(B\right)$, because tall persons are more inclined to do so. As a result, from least to largest, the order is: $P\left(B\right)<P(B/T)<P\left(T\right)<P(T/B)$