# 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%.

Result

p1 =  15.1 %
p2 =  0.6 %

#### Solution:

$p_1 = 100\% \cdot {{ 7} \choose 5} \cdot \left( \dfrac{ 48.69}{100} \right)^{ 5} \cdot \left(\dfrac{ 51.31}{100}\right)^{ 7-5} \doteq 15.1 \\%$
$p_2 = 100\% \cdot {{ 7} \choose 7} \cdot \left( \dfrac{ 48.69}{100} \right)^{ 7} \cdot \left(\dfrac{ 51.31}{100}\right)^{ 7-7} \doteq 0.6 \\%$

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