Question 1154579
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            The simplest way to solve this problem is,  probably,  to use the sample space conception.



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(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 = {{{favorable/total}}} = {{{1/2}}}.




(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 = {{{favorable/total}}} = {{{1/2}}}.
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Solved.