Probability from a Sample Space. In Exercises 33–36, use the given sample space or construct the required sample space to find the indicated probability.

Four Children Using the same sample space and assumption from Exercise 35, find the probability that when a couple has four children, all four are of the same gender.

A couple has four children.

Theprobability of an eventis a number that quantifies the possible occurrence of an event.

Its formula is written below:

$P\left(A\right)=\frac{\text{Number}\text{of}\text{outcomes}\text{that}\text{favour}\text{A}}{\text{Total}\text{number}\text{of}\text{outcomes}}$

Sample space is exhaustive of all possible events.

Refer to Exercise 35; the sample space has 16 outcomes shown below.

The total number of gender combinations = 16.

The sample space of the genders of four children to be given as follows:

S=(bbbb,bbbg,bbgb,bgbb,gbbb,bbgg,bgbg,gbgb,ggbb,bggb,gbbg,gggb,ggbg,gbgg,bggg,gggg)

The number of combinations that have the same gender for all four children is two. They are (bbbb, gggg).

The probability of event E, same-gender for all four children, is calculated as shown below:

$$\begin{gathered} P\left(E\right)=\frac{2}{16} \\ =0.125 \end{gathered}$$

Therefore, the probability of having the same gender for all four children is equal to 0.125.