SOLUTION: Determine the probabilities of having (a) at least 1 girl (a) at least 1 girl and 1 boy in a family of 4 children, assuming equal probability of male and female birth

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Question 1186589: Determine the probabilities of having
(a) at least 1 girl
(a) at least 1 girl and 1 boy in a family of 4 children, assuming equal probability of male and female birth
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
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Determine the probabilities of having
(a) at least 1 girl
(b) at least 1 girl and 1 boy in a family of 4 children, assuming equal probability of male and female birth
~~~~~~~~~~~~~~~ 


(a)  With 4 children in a family, there are, in total,  = 16 possible different configurations of boys/girls.


     Of them, there is only one "unfavorable" configuration, when all the children are boys.

     All other 15 configurations have at least one girl.


     So, there are 16 total configurations and of them, there are 15 favorable, having at least one girl.


     THEREFORE, the probability to have at least one girl in a family with 4 children 

                is  .          ANSWER




(b)  Again, there are 16 possible different configurations, in all.

   
     Of them, "unfavorable" are only 2 (two), having all 4 boys  OR  having all 4 girls.


     The rest 16-2 = 14 configurations are "favorable" : they have at least one boy and at least one girl.


     
     THEREFORE, the probability to have at least one girl AND at least one boy in a family with 4 children 

                is   = .      ANSWER

Solved and thoroughly explained.



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