Answer :

A couple has two children.

The sample space S = {(B,B),(B,G),(G,B),(G,G)}

Let P(A) be the probability of both being boys.

(i) Let P(B) be the probability of one of them being a boy.

The sample space of B ={(B,B),(B,G),(G,B)}

Let be the probability of one of them being a boy and both being boys.

*Tip – By conditional probability,* *where* *is the probability of occurrence of the event A given that B has already occurred.*

The probability that both are boys given that one of them is a boy:

(ii) Let P(B) be the probability of the elder being a boy.

The sample space of B ={(B,B),(B,G)}

Let be the probability of the elder being a boy and both being boys.

*Tip – By conditional probability,* *where* *is the probability of occurrence of the event A given that B has already occurred.*

The probability that both are boys given that the elder is a boy:

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