Question

Out of $800$ families with $4$ children each, the expected number of families having $2$ boys and $2$ girls

• A. $100$
• B. $200$
• C. $300$
• D. $400$

Answer 1

The correct option is C $300$

The probability of having a girl $=$probability of having a boy$=$$\frac{1}{2}$
The probability of exactly $2$ boys and two girls out of $4$ children is
${}^4{C}_2\left(\frac{1}{2}{)}^2\right(\frac{1}{2}{)}^2$

$=\frac{6}{2^4}$ $=\frac{6}{16}$ $=\frac{3}{8}$

Hence the required expectancy
$=800\left(\frac{3}{8}\right)$
$=3\left(100\right)$
$=300$