Question

A car dealership is offering an interesting incentive in order to get people to come and test drive its new sports cars. Everyone who agrees to a test drive gets to choose a key. There are 75 car keys in the bag, and 4 of them unlock a sports car. For the customers who choose a winning key, the dealership agrees to knock $1000 off of the price if they buy a new car. (Assume that each key is returned after being drawn.)

A) From the perspective of the car dealership, what is the expected value of the incentive for one customer who chooses a key and buys a new car?

B) If 90 customers come in and choose a key and all of them buy new cars, how much can the dealership expect to give up in sales?

Answer 1

The expected value of the incentive for one customer is $53.33. If 90 customers choose a key and buy new cars, the dealership can expect to give up $4800 in sales.

Step-by-step explanation:

A) The expected value of the incentive for one customer who chooses a key and buys a new car can be calculated by multiplying the probability of winning ($1000 off) by the cost of winning (4 out of 75 keys). The probability of winning is 4/75, and the cost of winning is $1000.

Expected value = (Probability of winning) x (Cost of winning) = (4/75) x $1000 = $53.33

Therefore, the expected value of the incentive for one customer is $53.33.

B) If 90 customers come in and choose a key and all of them buy new cars, the dealership can expect to give up (90 x $53.33) = $4800 in sales.