SOLUTION: Assume that each child who is born is equally likely to be a boy or a girl. If a family has two children, what is the probability that both are girls given that (a) the eldest is a

Question 1154579: Assume that each child who is born is equally likely to be a boy or a girl. If a family has two children, what is the probability that both are girls given that (a) the eldest is a girl, (b) atleast one is a girl?
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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The simplest way to solve this problem is, probably, to use the sample space conception.

(a)  In this case, the sample space consists of two pairs, ordered by the age 


         (youngest,eldest) = (boy,girl)  and  (youngest,eldest) = (girl,girl).


     Both these pairs (both elements of the sample space) are equally likelihood.

     The favorable pair is only one (youngest,eldest) = (girl,girl).


     Therefore, the probability in case (a)  P =  = .




(b)  In this case, the sample space consists of two pairs 


         (boy,girl)  and  (girl,girl)    (the order in pairs does not matter).


     Both these pairs (both elements of the sample space) are equally likelihood.

     The favorable pair is only one (girl,girl).


     Therefore, the probability in case (b)  P =  = .

Solved.

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