Figuring out which payment plan is the best and why

Question

you have been paying a delivery service $6 per week to make regular deliveries to your house. One week, just to make things interesting, you offer the service a new payment plan. Each week, you will allow the delivery person to reach into a paper bag and pull out two bills. The bag will contain one $10 bill and five $1 bills.

 

A. What are the two possible amounts you could pay under this new payment plan?

B. What is the probability of paying each of these amounts on any given week?

C. What is the average amount you will pay per week in the long run (i.e., the expected value) under the new plan?

D. Which payment plan would you choose?

Answer 1

A. $11 or $2

B. 5/6 probability of $2, 1/6 prob of $11

C. (5/6)(2) + (1/6)(11) = 21/6 = $3.50

D. "You (payer)" should choose the new plan because it would save $2.50 per week, on the average.