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A family has 2 children. Find the probability that both are boys, if it is known that (i) at least one of the children in a boy, (ii) the elder child is a boy.

A family has 2 children. Find the probability that both are boys, if it is known that

(i) at least one of the children in a boy,
(ii) the elder child is a boy.

Grade:

1 Answers

Latika Leekha
askIITians Faculty 165 Points
6 years ago
It is given that the family has two children.
Let A denote the event that both the children are boys.
Then, this is a cse of conditioinal probability.
(i) Let B be the event that that atleast one of the child is a boy.
Then, P(A/ B) = P (A and B) / P(B)
= P (both the children are boys / atleast one is a boy)
By definition of conditional probability, we have
P(A / B) =
P (both the children are boys and atleast one is a boy) / P(atleast one is a boy)
= P (Both the children are boys) / P( atleast 1 is a boy)
= (1/4) /(3/4)
= 1/3.
(ii) Let D be the event that that the elder child is a boy.
Then, P(A/ D) = P (A and D) / P(D)
= P (both the children are boys / elder one is a boy)
By definition of conditional probability, we have
P(A / D) =
P (both the children are boys and elder one is a boy) / P(elder child is a boy)
= P (Both the children are boys) / P( elder child is a boy)
= (1/4) / (1/2)
= 1/2.
Thanks & Regards
Latika Leekha
askIITians Faculty

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