Scenario 5.2:
Randy and Samantha are shopping for new cars (one each). Randy expects to pay $15,000 with 1/5 probability and $20,000 with 4/5 probability. Samantha expects to pay $12,000 with 1/4 probability and $20,000 with 3/4 probability.
-Refer to Scenario 5.2. Which of the following is true?
A) Randy has a higher expected expense than Samantha for the car.
B) Randy has a lower expected expense than Samantha for the car.
C) Randy and Samantha have the same expected expense for the car, and it is somewhat less than $20,000.
D) Randy and Samantha have the same expected expense for the car: $20,000.
E) It is not possible to calculate the expected expense for the car until the true probabilities are known.

Question

Quizplus · Accepted Answer

To calculate the expected expense for Randy, we use the formula:
Expected expense = (Probability of paying $15,000 x $15,000) + (Probability of paying $20,000 x $20,000)
Expected expense = (1/5 x $15,000) + (4/5 x $20,000)
Expected expense = $4,500 + $16,000
Expected expense = $20,500

To calculate the expected expense for Samantha, we use the formula:
Expected expense = (Probability of paying $12,000 x $12,000) + (Probability of paying $20,000 x $20,000)
Expected expense = (1/4 x $12,000) + (3/4 x $20,000)
Expected expense = $3,000 + $15,000
Expected expense = $18,000

Therefore, Randy has a higher expected expense than Samantha for the car.

Scenario 5.2: Randy and Samantha Are Shopping for New Cars (One Each)