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15. Suppose a law is passed which restricts the number of children a couple can have to be no more than 2. If the first child is a boy, then they may not have a second child. Otherwise they may have a second child. Suppose the probability of a male birth is 1/2 and the gender of children are independent. Assume all couples want to have as many children as they can. (i). What is the sample space of the children a couple could have. (ii). Let X denote the number of girls in a family. What's the probability distribution of X?

15. Suppose a law is passed which restricts the number of children a couple can have to be no more than 2. If the first child is a boy, then they may not have a second child. Otherwise they may have a second child. Suppose the probability of a male birth is 1/2 and the gender of children are independent. Assume all couples want to have as many children as they can. (i). What is the sample space of the children a couple could have. (ii). Let X denote the number of girls in a family. What's the probability distribution of X?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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For this practice, my teacher says the following answers are below. However, I don't know how he got these answers. Please explain.

i) S = {B, GB, GG}

ii) X               0     1     2
   Probability 1/2 1/4 1/4  

iii) ?? = ? × ?.? + ? × ?.?? + ? × ?.?? = .??

iv) ?? + ?? = ??? + ??? = ?.?? + ?.?? = ?.?

15. Suppose a law is passed which restricts the number of children a couple can have to be no more than 2. If the first child is a boy, then they may not have a second child. Otherwise they may have a second child. Suppose the probability of a male birth is 1/2 and the gender of children are independent. Assume all couples want to have as many children as they can. (i). What is the sample space of the children a couple could have. (ii). Let X denote the number of girls in a family. What's the probability distribution of X? (iii). Find the expected value of X. (iv). Let X, denote the number of girls in family A and X2 the number of girls in family B. What is the expected value of X1 + X2?
Transcribed Image Text:15. Suppose a law is passed which restricts the number of children a couple can have to be no more than 2. If the first child is a boy, then they may not have a second child. Otherwise they may have a second child. Suppose the probability of a male birth is 1/2 and the gender of children are independent. Assume all couples want to have as many children as they can. (i). What is the sample space of the children a couple could have. (ii). Let X denote the number of girls in a family. What's the probability distribution of X? (iii). Find the expected value of X. (iv). Let X, denote the number of girls in family A and X2 the number of girls in family B. What is the expected value of X1 + X2?
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