Question

Out of $800$ families with $4$ children each, the expected number of families having atleast one boy is

• A. $550$
• B. $50$
• C. $750$
• D. $300$

Answer 1

Answer: (C)

$750$

The probability of having a girl$=$probability of having a boy$=$$\frac{1}{2}$
The probability of having no girl at all is equal to the probability of having at-least one boy
$=1-{}^4{C}_0\left(\frac{1}{2}{)}^0\right(\frac{1}{2}{)}^4$
$=1-\frac{1}{2^4}$
$=\frac{15}{16}$
Hence, the required expectancy
$=800\left(\frac{15}{16}\right)$
$=15\left(50\right)$
$=750$