Question

Scenario 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 2. Which of the following is true? 

A. Randy and Samantha have the same expected expense for the car: $20,000. 

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

C. Randy has a lower expected expense than Samantha for the car. 

D. Randy and Samantha have the same expected expense for the car, and it is somewhat less than $20,000 

E. It is not possible to calculate the expected expense for the car until the true probabilities are known.

Answer 1

Randy expects to pay $15000 with 1/5 probability and $20,000 with 4/5 probability.

=> Randy expected expenses = (1/5) * ($15000) + (4/5) * ($20,000)

=> Randy expected expenses = $3000 + $16,000

=> Randy expected expenses = $19,000

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Samantha expects to pay $12,000 with 1/4 probability and $20,000 with 3/4 probability.

=> Samantha expected expenses = (1/4) * ($12,000) + (3/4) * ($20,000)

=> Samantha expected expenses = $3,000 + $15,000

=> Samantha expected expenses = $18,000

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Randy has a higher expected expenses than Samantha for the car.

Answer: option (B)