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 isA. 1/2B. 1/3C. 2/3D. 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(MN) = 4

Now,

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