Question

Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at random. The probability that the eldest child is a girl given that the family ahs at least one girl is

A. 1/2

B. 1/3

C. 2/3

D. 4/7

Answer 1

Correct option is D. 4/7

The sample set we have, where the first letter represents the eldest child of the family→

S = { GGG, GBG, GGB, GBB , BBB, BBG, BGB, BGG }

Now let,

M = Event of choosing a family with a girl as the eldest child.

= { GGG, GBG, GGB, GBB }

N = Event of choosing a family with at-least one girl child.

= { GGG, GBG, GGB, GBB, BBG, BGB, BGG }

We have,

n(M)= 4

n(N) = 7

n(M∩N) = 4

Now,