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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)}
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
To find P(E|F)
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
E ∩ F = {(b, b)}
P(E ∩ F ) = 1/4
P(E|F) = (( ∩ ))/(())
= (1/4)/(3/4)
= 1/3
∴
Required Probability is 1/3
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(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 females
F : elder child is a female
To find P(E|F)
E : both children are females
E = {(g, g)}
P(E) = 1/4
F : elder child is a female
F = {(g, b), (g, g)}
P(F) = 2/4=1/2
Also, E ∩ F = {(g, g)}
So, P(E ∩ F) = 1/4
P(E|F) = (( ∩ ))/(())
= (1/4)/(1/2)
= ½
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Hope It's Helpful.....:)