A couple has 3 children each child is equally likely to be a boy or a girl. The probability that the eldest child is a girl given that they have atleast one boy is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{3}{7}$
A = event that the eldest child is a girl , B = event that there is at least one boy
We need to find:
P(A|B) = P(A ∩ B) / P(B)
All possible outcomes for 3 children are: (BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG)
Total outcomes = 8
Event B: “at least one boy”
All outcomes except GGG satisfy this.
n(B) = 7
Event A ∩ B: Eldest child is a girl and there is at least one boy.
Possible outcomes: GBB, GBG, GGB
n(A ∩ B) = 3
Therefore, P(A|B) = 3/7