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Supposed (as is roughly correct) that each child born is equally likely to be a boy or a girl and that sexes of successive children are independent. If we let BG mean that the older child is a boy, and the younger child is a girl, then each of the combinations BB, BG, GB, GG has probability 0.25. Ashley and Brianna each have two children. a.) You know that at least one of Ashley's children is a boy. What is the conditional probability that she has two boys? b.) You know that Brianna's older child is a boy. What is the conditional probability that she has two boys? please help, if you can :)

Started by xperry ( Everest College-Colorado Springs )

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a.) The conditional probability that Ashley has two boys given that at least one of her children is a boy is 0.5. This is because the probability that both of her children are boys (BB) is 0.25, and that the probability that one of her children is a boy and one is a girl (BG) is also 0.25. Because these events are mutually exclusive and sum to one, the probability that at least one of her two children is a boy is 0.5. b.) The conditional probability that Brianna has two boys given that her older child is a boy is 1/3. This is because the conditional probability of the event that both of Brianna's children are boys (BB) given that her older child is a boy is 1/3. The other two possibilities are that her younger child is a girl (BG), which has probability 1/3, and that both of her children are girls (GG), which also has probability 1/3.

Answered by john89

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