Families 2

There are 729 families having 6 children each. The probability of a girl is 1/3 and the probability of a boy is 2/3. Find the the number of families having 2 girls and 4 boys.

Correct result:

n =  240

Solution:

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

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Showing 2 comments:

Math student

The correction notation is p = 6 combination 2 and not 2 combination 6

1 month ago  Like

Matematik

Thanks, we just exange 6 and 2

1 month ago  Like

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