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:

$\frac{3}{7}$

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