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Q.

Assume that each born child is equally likely to be either a boy or a girl. If a family has two children, What is the conditional probability that both are girls given that the youngest is a girl is $λ$ then $12 λ$ is----

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answer is 6.

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Detailed Solution

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$L e t E = {b o t h a r e g i r l s} = {G G}$

$n (E) = 1$

$t h e e v e n t E_{1} = {t h e y o u n g e s t i s a g i r l} = {G B, G G}$

$n (E_{1}) = 2$

$∴ E_{1} \cap E_{2} = {G G}$

$n (E_{1} \cap E_{2}) = 1$

$∴ P (E / E_{1}) = \frac{n (E \cap E_{1})}{n (E_{1})} = \frac{1}{2} = 0.5$

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Assume that each born child is equally likely to be either a boy or a girl. If a family has two children, What is the conditional probability that both are girls given that the youngest is a girl is λ then 12λ is----