Mark the correct alternative in each of the following:
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
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,