Question

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

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

Answer 1

The correct option is A $1875$

Given that, out of $2000$ families with $4$ children,

We can take the gender of the children then probability of being boy probability of being girl $=\frac{1}{2}$

According to given condition,

$probabilityofatleast1boy$ $=1-\left(probabilityallgirls\right)$

$=1-{\left(\frac{1}{2}\right)}^4$

$=1-\frac{1}{16}$

$=\frac{15}{16}$

So, expected number of families with criteria from a pool of $2000$ families

$=2000\times \frac{15}{16}$

$=125\times 15$

$=1875$

Hence, this is the answer.

option $\left(A\right)$ is correct.