Q. 12 4.2( 31 Votes )

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl?

Answer :

Let B denote boy and G denote girl.

Then, the sample space of the given experiment will be:


S = {GG, GB, BG, BB}


Let E be the event that ‘both are girls’.


E = {GG}



(i) Let F be the event that ‘the youngest is a girl’.


F = {GG, BG}


……….(I)


Now, E F = {GG}


……….(II)


Now, we know that


By definition of conditional probability,



[Using (I) and (II)]



(ii) Let H be the event that ‘at least one is a girl’.


H = {GG, GB, BG}


……….(III)


Now, E H = {GG}


……….(IV)


Now, we know that


By definition of conditional probability,



[Using (III) and (IV)]



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