Question

Out of $2000$ families with $4$ children, the number of families you expect to have at least one boy is

• A. $1875$
• B. $750$
• C. $1250$
• D. $625$

Answer 1

Answer: (A)

$1875$

The probability of $4$ families having at-least one boy will be
$1-{}^4{C}_0(\frac{1}{2}{)}^4$

$=1-\frac{1}{16}$ $=\frac{15}{16}$
Hence the expected frequency for $2000$ families is
$=2000\left(\frac{15}{16}\right)$

$=125\left(15\right)$
$=1875$