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 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 children financial assistance to buy a car and to pay rent. a. Develop a joint probability table and use it to answer the remaining questions (to 2 decimals). b. Using the marginal probabilities for buy a car and pay rent (to 2 decimals). c. If parents provided financial assistance to buy a car, what it the probability that the parents assisted with paying rent (to 4 decimals)? d. If parents did not provide financial assistance to buy a car, what is the probability the parents assisted with paying rent (to 4 decimals)? e. Is financial assistance to buy a car independent of financial assistance to pay rent? Use probabilities to justify your answer. f. What is the probability that parents provided financial assistance for their adult children by either helping buy a car or pay rent (to 2 decimals)?

Explanation / Answer

// COMPLETE SOLUTION

a.
. . . . . . . . . . . . Pay Rent
. . . . . . . . . . . . Yes . . . No . . Total
Buy . . . Yes ... 0.28 ... 0.26 ... 0.54
a car . . No .... 0.07 ... 0.39 ... 0.46
. . . . . Total .... 0.35 ... 0.65 ... 1.00

b.
P(parents assist in buying car) = 0.54
P(parents assist in paying rent) = 0.35
More likely to assist with buying a car

c)

P(Pay rent | Buy car) = P(Buy car + Pay rent)/ P(Buy car) =

                                     = (56/200)/(108/200)

                                     = 0.5185

d)

P(Pay rent | ~Buy car) = P(~Buy car + Pay rent)/ P(~Buy car) =

                                     = (14/200)/(92/200)

                                     = 0.1522

e.
Define two events:
C - parents assist in buying car
R - parents assist in paying rent
Two events are independent iff their joint probability = the product of their probabilities
P(C+R) = 0.28
P(C) * P(R) = 0.54 * 0.35 = 0.189

NO, financial assistance to buy a car is NOT independent of financial assistance to pay rent

f.
P(C or R) = P(C) + P(R) - P(C?R) = 0.54 + 0.35 ? 0.28 = 0.61
Alternatively:
P(C or R) = 1 ? P(no assistance) = 1 ? 0.39 = 0.61

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