(12.42) Choose at random a person aged 15 to 44 years. Ask their age and who the

Question

(12.42) 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: AloneWith spouseWith others ( not a spouse) 15 - 190.0010.0010.16320 - 240.0120.0220.13725 - 340.0320.1470.15435 - 440.0270.2110.093 15 - 1920 - 2425 - 3435 - 44Alone0.0010.0120.0320.027With spouse0.0010.0220.1470.211With others ( not a spouse) 0.1630.1370.1540.093 (a) Is this is a legitimate finite probability model: Yes No (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)?

Explanation / Answer

The probability distribution is:

a) All probabilities are between 0 and 1. Also,

Sum = 1

So,

Yes, This is a legitimate finite probability model.

b) P(Person chosen is 15-19 years old who lives with others) = 0.163

c) P(Person is 15-19 years old) = 0.001 + 0.001 + 0.163 = 0.165

d) P(Person chosen lines with others) = 0.163 + 0.137 + 0.154 + 0.093 = 0.547

Age Group Probabilities Alone With Spouse With Others 15-19 0.001 0.001 0.163 20-24 0.012 0.022 0.137 25-34 0.032 0.147 0.154 35-44 0.027 0.211 0.093

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