300 CHAPTER 12 Introducing Probability Choose at random a person aged 15 to 44 y

Question

300 CHAPTER 12 Introducing Probability Choose at random a person aged 15 to 44 years. Ask their age and who they live with (alone, with spouse, with other persons). Here is the probability model for 12 possible answers:14 ra AGE IN YEARS 15-19 20-24 25-34 35-44 0.001 0.010 0.032 0.028 0.001 0.021 0.151 0.208 12.47 w Alone With spouse With others (not a spouse) 0.168 0.139 0.149 0.092 Exercises 12.42 to 12.44 use this probability model. 12.42 Living arrangements. (a) Why is this a legitimate finite probability model? (b) What is the probability that the person chosen is a 15- to 19-year-old who lives with others (not a spouse)? (c) What is the probability that the person is 15 to 19 years old? (d) What is the probability that the person chosen lives with others (not a spouse)? 12.48

Explanation / Answer

Ans:

Joint probability distribution and marginal probabilities(Total):

a)It is legitomate probability distribution,as sum of all enteries is 1.

b)P(15-19 and lives with others)=0.168

For part c and d,first get

Marginal probabilities:

P(alone)=0.071,P(with spouse)=0.381,P(with others)=0.548

P(15-19)=01.7,P(20-24)=0.17),P(25-34)=0.332,P(35-44)=0.328

c)P(15-19)=0.17

d)P(with others)=0.548

For part b) if the statement was Probability of a person who lives with others given that of 15-19,

Then P(with others/15-19)=P(with others and 15-19)/P(15-19)=0.168/0.17 =0.9882

15-19 20-24 25-34 35-44 Total Alone 0.001 0.01 0.032 0.028 0.071 with spouse 0.001 0.021 0.151 0.208 0.381 with others 0.168 0.139 0.149 0.092 0.548 Total 0.17 0.17 0.332 0.328 1

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