Consider a family with two children. Assume that each child is as likely to be a boy as it is to be a girl. Find the conditional probability that both children are boys, given that one child is a boy

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Solution

The correct option is A $1 / 2$
$P (b o y) = 1 / 2 = P (g i r l)$
$P (2 b o y s) = (\frac{1}{2})^{2} = \frac{1}{4}$
$P (2 b o y s | 1 b o y) = P (2 b o y) / P (1 b o y) = 1 / 2$

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Consider a family with two children. Assume that each child is as likely to be a boy as it is to be a girl. Find the conditional probability that both children are boys, given that one child is a boy

The correct option is A 1/2P(boy)=1/2=P(girl)P(2 boys)=(12)2=14P(2 boys|1 boy)=P(2 boy)/P(1 boy)=1/2

The correct option is A $1 / 2$
$P (b o y) = 1 / 2 = P (g i r l)$
$P (2 b o y s) = (\frac{1}{2})^{2} = \frac{1}{4}$
$P (2 b o y s | 1 b o y) = P (2 b o y) / P (1 b o y) = 1 / 2$