Misc 2 - A couple has two children (i) Probability both are males - Miscellaneous

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Misc 2 A couple has two children, (i) Find the probability that both children are males, if it is known that at least one of the children is male. A Couple has two children, Let boy be denoted by b & girl be denoted by g So, S = {(b, b) ,(b, g),(g, b), (g, g)} We need to find probability that both children are males, if known that at least one of children is male Let E : Both children are males F : At least one child is male We need to find P(E|F) Also, E ∩ F = {(b, b)} P(E ∩ F ) = 1﷮4﷯ P(E|F) = 𝑃(𝐸 ∩ 𝐹)﷮𝑃(𝐹)﷯ = 1﷮4﷯﷮ 3﷮4﷯﷯ = 1﷮3﷯ ∴ Required Probability is 𝟏﷮𝟑﷯ Misc 2 A couple has two children, (ii) Find the probability that both children are females, if it is known that the elder child is a female A Couple has two children, Let boy be denoted by b & girl be denoted by g So, S = {(b, b) ,(b, g),(g, b), (g, g)} We need to find the probability that both children are females, if from that the elder child is a female. Let E : both children are females F : elder child is a female We need to find P(E|F) Also, E ∩ F = {(g, g)} So, P(E ∩ F) = 1﷮4﷯ P(E|F) = 𝑃(𝐸 ∩ 𝐹)﷮𝑃(𝐹)﷯ = 1﷮4﷯﷮ 2﷮4﷯﷯ = 1﷮2﷯ ∴ Required probability is 𝟏﷮𝟐﷯

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