Chapter 13.3, Problem 37AYU

In Problems 37-40, assume equally likely outcomes.

Determine the probability of having 3 boys in a 3-child family.

To determine

The probability of having 3 boys in a 3-child family.

Answer to Problem 37AYU

$P\left(3 Boys\right)=\frac{1}{8}$

Explanation of Solution

Given:

A family has 3 children. Assume equally likely outcomes.

Formula used:

If $S$ is the sample space of this experiment,

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

Calculation:

The sample space $S=\left\{BBB,BBG,BGB,BGG,GBB,GBG,GGB,\text{}GGG\right\}$.

$E=\left\{BBB\right\}$

$P\left(3 Boys\right)=\frac{n\left(E\right)}{n\left(S\right)}$

$P\left(3 Boys\right)=\frac{1}{8}$