Question

The probability that in a family of $4$ children there will be atleast one boy is

• A. $\frac{13}{16}$
• B. $\frac{15}{16}$
• C. $\frac{14}{16}$
• D. $\frac{12}{16}$

Answer 1

The correct option is B $\frac{15}{16}$

A child can be boy or a girl
So, $p=q=\frac{1}{2},n=4$ (given)
$\Rightarrow P(X\ge 1)=$ probability of atleast one boy $=1-$ (probability of all children are girl
$\Rightarrow P(X\ge 1)=1-P(X=0)=1-{\left(\frac{1}{2}\right)}^4=\frac{15}{16}$