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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.