Question

Out of $10,000$ families with $4$ children each, the expected number of families all of whose children are daughters is

• A. $225$
• B. $400$
• C. $625$
• D. $125$

Answer 1

The correct option is C $625$

$P(X=Girl)=\frac{1}{2}$

Probabilty of all $4$ childrens girl $=$ $\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{16}$

Expected number of families $=$ $np=10000\times \frac{1}{16}=625$