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Probability

Question
CBSEENMA12033619

A couple has two children,
Find the probability that both children are males, if it is known that at least one of the children is male. 

Solution

S = {MM, MF, FM, FF}
where M stands for male and F stands for female
  Let A: both the children are males
and B: at least one of the children is male.
 therefore    A = {MM},   B = {MM, MF, FM}
therefore space space space space straight A space intersection straight B space equals space left curly bracket MM 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 3 over 4 comma space space straight P left parenthesis straight A intersection straight B right parenthesis space equals space 1 fourth
Required probability  = straight P left parenthesis straight A space left enclose straight B right parenthesis space equals space fraction numerator straight P left parenthesis straight A intersection 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 3 over 4 end style end fraction space equals 1 third

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