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The possible combinations of children when a couple has three children is given as (bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg), where b means a boy, and g means a girl.

Theprobability of an event is a value that measures the chance of an event happening. It has the given formula:

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

The set of all outcomes of an event is called thesample space.

Let S be the sample space for the genders of three children as shown below:

S =(bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg), where b represents a boy, and g represents a girl.

The total number of combinations of genders = 8

The number of combinations that contain only one girl is equal to three. They are (bbg, gbb, bgb).

The probability of event E; only one girl out of three children is calculated as shown:

$$\begin{gathered} P\left(E\right)=\frac{3}{8} \\ =0.375 \end{gathered}$$

Therefore, the probability of only one girl out of three children is equal to 0.375.