SOLUTION: A couple plan to have children, one a year, until they either have two boys or four children. Assume either gender is equally likely. Find the probability that they will have exact

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Question 267277: A couple plan to have children, one a year, until they either have two boys or four children. Assume either gender is equally likely. Find the probability that they will have exactly three children, given that the second child is a girl.
Answer by solver91311(24713) About Me  (Show Source):
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If the second child is a girl, the only possible way to have two boys in a total of three children is for the first and third to be a boy. Since we are presuming that it is still possible after the first two children are born to have two boys in a total of three children, then it is certain that the first is a boy. Hence, the probability of the couple having exactly three children is the same as the probability that the third child is a boy, that is, 0.5


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