SOLUTION: Given a family with three children, find the probability of the event. given that the birth order alternates between girls and boys. What is the probability that the youngest is a

Question 1164268: Given a family with three children, find the probability of the event.
given that the birth order alternates between girls and boys. What is the probability that the youngest is a boy, given that the birth order alternates between girls and boys?
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

There are 2*2*2 = 8 possible boy/girl sequences.

Of those 8, only two are sequences in which the birth order alternates between boys and girls: BGB and GBG.

Of those two, only one has a boy as the youngest.

ANSWER: The probability that the youngest is a boy, given that the birth order alternates between boys and girls, is 1/2.

More formally, using the definition of conditional probability, theprobability that the youngest is a boy, given that the birth order alternates between boys and girls, is:



 P((birth order alternates between boys and girls)AND(youngest is a boy))    (1/8) =  1

-------------------------------------------------------------------------- = ----- = ---

           P(birth order alternates between boys and girls)                  (2/8) =  2 

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