Dear Mayank

Given at least 1 child in a family with 3 children is a boy

so event  1 boy in a family  ,2 boy in a family ,  3 boy in a fimily are equally likily event

 so chances of happening any event fou of three is 1/3

 so prob that family have 2 of the children are boys =1/3

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Badiuddin

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.