A couple has 3 children and it is known that atleast one of them is a boy. Then the probability that the couple will have exactly two boys is 

A couple has 3 children 

$\mathrm{E}=\mathrm{atleast} \mathrm{one} \mathrm{of} \mathrm{the} 3 \mathrm{children} \mathrm{is} \mathrm{a} \mathrm{boy}.$

$\mathrm{F}= \mathrm{the} \mathrm{couple} \mathrm{will} \mathrm{have} \mathrm{exactly} \mathrm{two} \mathrm{boys}$

$n\left(E\right)={ }^3{C}_1+{{ }^3{C}_2+}^3{C}_3=7$

$n\left(E\cap F\right)={ }^3{C}_2=3$

$P\left(F/E\right)=\frac{n\left(E\cap F\right)}{n\left(E\right)}=\frac{3}{7}$