Question 866158
Let A  be the event "the family has children of only one sex".
Let B  be the event "the family has children of both sexes".
It's clear that 
{{{P(A)+P(B)=1}}}
There are 16 possible combinations of sexes from MMMM, MMMF, through, FFFM, FFFF.
Only two fall into the A category {MMMM,FFFF} so,
{{{P(A)=2/16=1/8}}}
So then,
{{{P(B)=1-P(A)}}}
{{{P(B)=1-1/8}}}
{{{P(B)=7/8}}}