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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. (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,(i) Find the probability that both children are males, if it is known that at least one of the children is male.(ii) Find the probability that both children are females, if it is known that the elder child is a female.

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3 months ago Anand Kumar Pandey
2937 Points
```							Dear StudentA couple has two children,Let boy be denoted by b & girl be denoted by gSo, S = {(b, b) ,(b, g),(g, b), (g, g)}To find probability that both children are males,if known that at least one of children is maleLet E : Both children are malesF : At least one child is maleTo find P(E|F)E : Both children are malesE = {(b, b)}P(E) = 1/4F : At least one child is maleF = {(b, g), (g, b), (b, b)}P(F) = 3/4E ∩ F = {(b, b)}P(E ∩ F ) = 1/4P(E|F) = (𝑃(𝐸 ∩ 𝐹))/(𝑃(𝐹))= (1/4)/(3/4)= 1/3∴ Required Probability is 𝟏/𝟑(ii) Find the probability that both children are females, if it is known that the elder child is a female.S = {(b, b) ,(b, g),(g, b), (g, g)}To find the probability that both children are females, if from that the elder child is a female.Let E : both children are femalesF : elder child is a femaleTo find P(E|F)E : both children are femalesE = {(g, g)}P(E) = 1/4F : elder child is a femaleF = {(g, b), (g, g)}P(F) = 2/4=1/2Also, E ∩ F = {(g, g)}So, P(E ∩ F) = 1/4P(E|F) = (𝑃(𝐸 ∩ 𝐹))/(𝑃(𝐹))= (1/4)/(1/2)= ½Thanks
```
3 months ago
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