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

Misc 2 - Chapter 13 Class 12 Probability - Part 2

 

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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 E : Both children are males E = {(b, b)} P(E) = 1/4 F : At least one child is male F = {(b, g), (g, b), (b, b)} P(F) = 3/4

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