Question

Tall people and basketball players Select an adult at random. Define events T: person is over $6$feet tall, and

B: person is a professional basketball player. Rank the following probabilities from smallest to largest. Justify your answer.

$P(\mathrm{T})P(B)P(T\mid B)P(\mathrm{B}\mid \mathrm{T})$

Short answer

The correct order is$P(\mathrm{B})<P(\mathrm{B}\mid \mathrm{T})<P(\mathrm{T})<P(\mathrm{T}\mid \mathrm{B})$

Step-by-step solution

Given Information

It is given that:

T: Person is over sic feet tall.'

B: Person is professional basketball player.

$P(\mathrm{T})$ Probability of person is over six feet

$P(\mathrm{B})$ Probability for professional basketball player

$P(\mathrm{B}\mid \mathrm{T})$ Conditional probability for over six feet tall basketball player

$P(\mathrm{T}\mid \mathrm{B})$ Conditional probability for professional basketball player over six feet tall

Explanation

As per universal fact, most basketball player are very tall.

$P(\mathrm{T}\mid \mathrm{B})$is largest as there are lot of tall people.

$P(\mathrm{T})$is next largest as most tall people do not play basketball.

$P(\mathrm{B}\mid \mathrm{T})<P\left(T\right)$as tall people are more likely to play basketball.

Hence,$P(\mathrm{B}\mid \mathrm{T})>P\left(B\right)$

The correct order is$P(\mathrm{B})<P(\mathrm{B}\mid \mathrm{T})<P(\mathrm{T})<P(\mathrm{T}\mid \mathrm{B})$