SOLUTION: In the certain city, 43% of all children born are boys and 57% are girls. What is the probability that the next 3 children born will be all girls? What is the probability that

Algebra ->  Probability-and-statistics -> SOLUTION: In the certain city, 43% of all children born are boys and 57% are girls. What is the probability that the next 3 children born will be all girls? What is the probability that      Log On


   

Question 1098697: In the certain city, 43% of all children born are boys and 57% are girls.
What is the probability that the next 3 children born will be all girls?
What is the probability that out of the next 4 children born that none will be girls?
What is the probability that out of the next 5 children born at least one is a girl?
Answer by ikleyn(52792) About Me  (Show Source):
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In the certain city, 43% of all children born are boys and 57% are girls.
What is the probability that the next 3 children born will be all girls?
What is the probability that out of the next 4 children born that none will be girls?
What is the probability that out of the next 5 children born at least one is a girl?
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Actually, the first phrase of this post is not relevant to the others.

The basic fact is that the probability of the birth of a boy or a girl is close to 1/2,
and in school math problems like this the value of 0.5 for the probability is used.

For the answer, it doesn't matter what is the current ratio of the numbers of boys and girls in a city. 

    1)  What is the probability that the next 3 children born will be all girls?     
                     
            It is   %281%2F2%29%5E3 = 1%2F2%5E3 = 1%2F8.



    2)  What is the probability that out of the next 4 children born that none will be girls?       

            It is   %281%2F2%29%5E4 = 1%2F2%5E4 = 1%2F16.



    3)  What is the probability that out of the next 5 children born at least one is a girl?           

            It is "the complement" to the probability that out of the next 5 children born all are boys. 

            Thus the probability under the question is equal to  1 - 1%2F2%5E5 = 31%2F32.