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Probability

Question
CBSEENMA12033620
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A couple has two children,
Find the probability that both children are females, if it is known that the elder child is a female.

Solution

S = {MM, MF, FM, FF}
where M stands for male and F stands for female
Let A: both the children are female
and B: elder child is a a female.
therefore space space space straight A space equals space left curly bracket FF right curly bracket comma space space straight B space equals space left curly bracket FM comma space FF right curly bracket therefore space space space straight A space intersection space straight B space equals space left curly bracket FF right curly bracket space equals space straight A therefore space space space straight P left parenthesis straight A right parenthesis space equals space 1 fourth comma space space straight P left parenthesis straight B right parenthesis space equals space 2 over 4 comma space space space straight P left parenthesis straight A space intersection straight B right parenthesis space equals space 1 fourth

Required probability = straight P left parenthesis straight A space left enclose space straight B end enclose right parenthesis space equals space fraction numerator straight P left parenthesis straight A space intersection space straight B right parenthesis over denominator straight P left parenthesis straight B right parenthesis end fraction space equals space fraction numerator begin display style 1 fourth end style over denominator begin display style 2 over 4 end style end fraction space space equals 1 half

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