Yuriy and Svetlana have 7 children. Find the probability that they have 2 girls.
State the answer as a reduced fraction or an exact decimal. Do not round the answer.

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Yuriy and Svetlana have 7 children. Find the probability that they have 2 girls. State the answer as a reduced fraction or an exact decimal. Do not round the answer.

UpStudy AI · Accepted Answer

The probability that Yuriy and Svetlana have exactly 2 girls out of 7 children can be calculated using the binomial probability formula:

$$
P(k \text{ girls}) = \binom{n}{k} \left(\frac{1}{2}\right)^n
$$

Where:
- $$ n = 7 $$ (total number of children)
- $$ k = 2 $$ (desired number of girls)
- $$ \binom{n}{k} $$ is the binomial coefficient, representing the number of ways to choose $$ k $$ girls out of $$ n $$ children.

First, calculate the binomial coefficient:

$$
\binom{7}{2} = \frac{7!}{2!(7-2)!} = \frac{7 \times 6}{2 \times 1} = 21
$$

Next, calculate the probability:

$$
P(2 \text{ girls}) = 21 \times \left(\frac{1}{2}\right)^7 = 21 \times \frac{1}{128} = \frac{21}{128}
$$

So, the probability is:

**$$\frac{21}{128}$$**
The probability of having exactly 2 girls out of 7 children is $$\frac{21}{128}$$.

Yuriy and Svetlana have 7 children. Find the probability that they have 2 girls.
State the answer as a reduced fraction or an exact decimal. Do not round the answer.

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