5. According to the Ameriprise Financial Money Across Generations study, 9 out o
ID: 3277899 • Letter: 5
Question
5. According to the Ameriprise Financial Money Across Generations study, 9 out of 10 parents 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. Pay Rent Yes No Buy a Car es 56 52 78 No 14 a. b. Develop a joint probability table and use it to answer the remaining questions Using the marginal probabilities for buy a car and pay rent, are parents more likely to assist their adult children with buying a car or paying rent? What is your interpretation of the marginal probabilities? If parents provided financial assistance to buy a car, what it the probability that the parents assisted with paying rent? If parents did not provide financial assistance to buy a car, what is the probability the parents assisted with paying rent? c. e. Is financial assistance to buy a car independent of financial assistance to pay rent? Use probabilities to justify your answer robability that parents provided financial assistance for their adult chil- dren by either helping buy a car or pay rent?Explanation / Answer
The total frequency here is computed as: = 56 + 52 + 14 + 78 = 200
Therefore the required joint probability distribution here is computed as:
b) Now the probability that a parent pays for rent is computed as: = 0.28 + 0.07 = 0.35
Probability that a parent pays for car = 0.28 + 0.26 = 0.54
Therefore it is more likely that the parents assist their children with buying a car than paying rent.
c) Given that the parents provides assistance to buy a car, probability that the parents assist with paying rent
= Probability that parents provides assistance to buy a car as well as rent / Probability that the parent provides assistance in buying a car
= 0.28 / 0.54
= 0.5185
Therefore 0.5185 is the required probability here.
d)Given that the parents do not provides assistance to buy a car, probability that the parents assist with paying rent
= Probability that parents provides assistance to pay rent but not buying car / Probability that the parent do not provides assistance in buying a car
= 0.07 / ( 0.07 + 0.39 )
= 0.1522
Therefore 0.1522 is the required probability here.
Pay rent Yes Pay rent No Buy a car Yes 56/200 = 0.28 52/200 = 0.26 Buy a car No 14/200 = 0.07 78/200 = 0.39Related Questions
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