According to the Ameriprise Financial Money Across Generations study, 9 out of 1

Question

According to the Ameriprise Financial Money Across Generations study, 9 out of 10 par- ents with adult children ages 20 to 35 have helped their adult children with some type of financial assistance ranging from college, a car, rent, utilities, credit-card debt, and/or down payments for houses (Money, January 2009). The following table with sample data consistent with the study shows the number of times parents have given their adult chil dren financial assistance to buy a car and to pay rent. 35, Pay Rent Yes 56 14 No Yes No 52 1o9 78 2 Buy a Car ????? 70 1301200. a. Develop a joint probability table and use it to answer the remaining questions. b. Using the marginal probabilities for buy a car and pay rent, are parents more Jlikely to assist their adult children with buying a car or paying rent? What is your interpreta- n of the marginal probabilities? c. parents provided financial assistance to buy a car, what it the probability, that the d. parents did not provide financial assistance to buy a car, what is the probability the e· lsfinancial assistance to buyacarindependentof financial assistanceto arent? Use f. What is the probability that parents provided financial assistance for their adult chil- arents assisted with paying rent parents assisted with paying rent? probabilities to justify your answer dren by either helping buy a carfor pay rent?

Explanation / Answer

a) The joint probabiltiy distribution is

b) The marginal probability distribution of Buy a car and Pay Rent is

c)

P(Paying Rent / Buy a car) = P(Paying Rent and Buy a car) / P(Buy a car)
= 0.28 / 0.54 = 0.5185

d) P(Paying Rent / not Buy a car) = P(Paying Rent and not Buy a car) / P(not Buy a car)
= 0.07 / 0.46 = 0.1522

e)
P(paying rent) P(Buy a car) = 0.54*0.35 = 0.189 which is not equal to 0.28 = P(paying rent and Buy a car)
Therefore they are not independent

f)
P(buy a car or pay rent) = P(buy a car) + P(pay rent) - P(buy a car and pay rent)
0.54 + 0.35 - 0.28 = 0.61

Pay Rent Yes No Buy a Car Yes 0.28 0.26 No 0.07 0.39

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