Q. 57

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

A. 1/2

B. 1/3

C. 2/3

D. 4/7

Answer :

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(MN) = 4


Now,



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