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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