You are responsible for purchasing 25 used cars for your company. Star Brand cars costs $7,500 and Diamond Brand cars cost $6,000. Based on experience, you believe that 20% of Star Brand cars are lemons (low quality) while 40% of Diamond Brand cars are lemons (low quality). You are willing to pay $5,000 for a known lemon and $12,000 for a known plum. Which brand do you purchase?

Question

Quizplus · Accepted Answer

For Diamond Brand cars, the cost per good car (plum) is $6,000, and the cost per lemon is $5,000. This means that the expected value for each car is:
$6,000 x 0.60 (probability of getting a good car) + $5,000 x 0.40 (probability of getting a lemon) = $5,800
For Star Brand cars, the cost per good car (plum) is $7,500, and the cost per lemon is $5,000. This means that the expected value for each car is:
$7,500 x 0.80 (probability of getting a good car) + $5,000 x 0.20 (probability of getting a lemon) = $6,800
Therefore, based on expected value, it is better to purchase Diamond Brand cars.

You Are Responsible for Purchasing 25 Used Cars for Your