Question

what is the probability of having atleast one boy in a family of 3 children?

Answer 1

If the family has 3 children, then they can be
{BBB, BBG, BGB, GBB, BGG, GBG, GBB, GGG}

total number of combinations = 8
number of combinations with atleast one boy = 7

Probability(atleast one boy) = 7/8

Answer 2

Some times it is simpler to calculate the contrary of the event and its probability and then subtract it from 1 to get our answer.
=====================
The probability of one child being a boy = 1/2      a girl = 1/2
Let us assume that the 3 children being boys or girls are independent events.

Event of having no boys at all
         = first child is a girl   AND    2nd child is a girl   AND  3rd girl is a girl.

P(no boys among 3 children) = 1/2 * 1/2 * 1/2 = 1/8
P(there is at least one boy among 3 children)  = 1  - 1/8 = 7/8