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Chapter 6: Problem 8

Make a list of all possible outcomes for gender when a family has two children. Assume that the probability of having a boy is \(0.50\) and the probability of having a girl is also \(0.50\). Find the probability of each outcome in your list.

Short Answer

Expert verified
The probabilities of each outcome for the family with two children are as follows: (BB) = 0.25, (BG) = 0.25, (GB) = 0.25, (GG) = 0.25.

Step by step solution

01

List the Possible Outcomes

The possible gender outcomes when a family has two children are: Boy - Boy (BB), Boy - Girl (BG), Girl - Boy (GB), and Girl - Girl (GG).
02

Calculate the Probability of each Outcome

Each childbirth event is an independent event, meaning the outcome of the first child's gender doesn't affect the outcome of the second child's gender. Given that the probability of having a boy (P(B)) is 0.50 and the probability of having a girl (P(G)) is also 0.50, the probability for each outcome can be calculated as follows:- Probability of (BB) = P(B) * P(B) = 0.50 * 0.50 = 0.25- Probability of (BG) = P(B) * P(G) = 0.50 * 0.50 = 0.25- Probability of (GB) = P(G) * P(B) = 0.50 * 0.50 = 0.25- Probability of (GG) = P(G) * P(G) = 0.50 * 0.50 = 0.25
03

Conclusion

So, in a family of two children, there is an equal \/ 0.25 probability of each outcome occurring: Two boys, a boy and a girl, a girl and a boy, or two girls.

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Most popular questions from this chapter

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