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A couple has four children. The genders of the four children need to be listed.

Sample spaceis the complete enumeration of all outcomes of an event.

On any particular order of childbirth, there are two possible outcomes, g(girl) or b(boy).

Therefore, on fourbirths, there would be ${\left(2\right)}^4=16$possible combinations.

Let S be the sample space for the gender of four children as shown below:

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

Theprobability of an event is a number that gives a sense of the likelihood of an event.

It has the following formula:

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

The total number of gender combinations = 16

The number of combinations that have three girls and one boy is equal to four. They are (gggb, ggbg, gbgg, bggg).

The probability of three girls and one boy (in any order) out of four children is calculated as shown:

$$\begin{gathered} P\left(\text{3}\text{girls and}\text{1}\text{boy}\right)=\frac{4}{16} \\ =0.25 \end{gathered}$$

Therefore, the probability of three girls and one boy (in any order) out of four children is equal to 0.25.