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)}
\(\therefore P(B)=\frac{3}{4}\)
Let P(A ∩ B) be the probability of one of them being a boy and both being boys
Tip – By conditional probability, P(A/B) = \(\frac{P(A \cap B)}{P(B)}\) where P(A/B) 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)}
\(\therefore P(B)=\frac{1}{2}\)
Let P(A ∩ B) be the probability of the elder being a boy and both being boys.
Tip – By conditional probability, P(A/B) = \(\frac{P(A \cap B)}{P(B)}\) where P(A/B) s 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:
