There is a probability that the family contains 1 boy,2boys or 3 boys.... so chance of each event selection is 1/3 but its not the final answer..
if one boy is there then chance of selecting that 1 boy from 3 children is 1/3
if 2 boys are there then chance of selecting one boy among them is 2/3
if 3 boys are there then chance of selecting 1 boy is 3/3 i.e., 1
Now, required probability is 1/3 * 1 / 1/3 * 1 + 1/3 * 2/3 +1/3 * 1/3 = 1/2
This is the final answer required.