Assume that in a family, each child is equally likely to be a boy or girls .A family with three children is is choosen at random. The probability that
Here, S={(B,B,G),(G,G,G),(B,G,G),(G,B,G),(G,G,B),(G,B,B),(B,G,B),(B,B,G)}
`E_(1)`=Event tht a family has atleast one girl, then
`E_(1)`={(G,B,B),(B,G,B),(B,B,G),(G,G,B),(B,G,G),(G,B,G),(G,G,G)}
`E_(2)`=Event that the eldest child is a girl, then
`E_(2)`={(G,B,B),(G,G,B),(G,B,G,),(G,G,G)}
`thereforeE_(1)capE_(2)`={(G,B,B),(G,G,B),(G,B,G),(G,G,G)}
`thereforeP(E_(2)//E_(1))=(P(E_(1)capE_(2)))/(P(E_(1)))=(4//8)/(7//8)=4/7`
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