Families 2

Seven hundred twenty-nine families have six children each. The probability of a girl is 1/3, and the likelihood of a boy is 2/3. Find the number of families having two girls and four boys.

Correct answer:

n =  240

Step-by-step explanation:

$$\begin{gathered} C_2(6)=\left(\genfrac{}{}{0ex}{}{6}{2}\right)=\frac{6!}{2!(6-2)!}=\frac{6\cdot 5}{2\cdot 1}=15 \\ p=\left(\genfrac{}{}{0ex}{}{6}{2}\right)\cdot (\frac{1}{3}{)}^2\cdot (\frac{2}{3}{)}^4=15\cdot (\frac{1}{3}{)}^2\cdot (\frac{2}{3}{)}^4=\frac{80}{243}\doteq 0.3292 \\ n=729\cdot p=729\cdot \frac{80}{243}=\frac{729\cdot 80}{243}=\frac{58320}{243}=240 \end{gathered}$$

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