# Family

What is the probability that a family with 7 childrens have:

1. exactly 5 girls?
2. 7 girls and 0 boys?

Consider the birth probability of a girl is 48.69% and boy 51.31%.

Correct result:

p1 =  15.1 %
p2 =  0.6 %

#### Solution:

${p}_{1}=100\mathrm{%}\cdot \left(\genfrac{}{}{0px}{}{7}{5}\right)\cdot {\left(\frac{48.69}{100}\right)}^{5}\cdot {\left(\frac{51.31}{100}\right)}^{7-5}\doteq 15.1\mathrm{%}$
${p}_{2}=100\mathrm{%}\cdot \left(\genfrac{}{}{0px}{}{7}{7}\right)\cdot {\left(\frac{48.69}{100}\right)}^{7}\cdot {\left(\frac{51.31}{100}\right)}^{7-7}\doteq 0.6\mathrm{%}$

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