Question
Download Solution PDFIn a family of three children, what is probability that the third child is a girl given that the other two are also girls?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula
Probability = Favourable outcome/total outcome
Calculation
Family of 3 children = G, G, G whereas G = Girls
We can select girl as 3C1 = \(\frac{3 !}{1! (3-1)!}\) = 3
No of possible ways to select the girls be \(\frac{^3 C _1}{2!}\)
⇒ Possible outcome = \(\frac 32\)
Total way to select girls =3! = 3 × 2
⇒ Total outcome 6
Probability = Favourable outcome/total outcome
⇒ Probability = \(\frac{3/2}{6}=\frac{3}{ 2 \times 6} = \frac 14\)
∴ The probability that the third child is a girl given that the other two are also girls is 1/4
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