You are making a hotel reservation and are offered a choice of two rates. The advanced purchase rate is $ 100, but your credit card will be charged immediately and there is no refund, even if you don’t use the room. The flexible rate is $ 140 but you don’t pay anything if you don’t use the room. Suppose p is the probability that you will end up using the room.
a. Suppose p = 0.70, so there is a 70% chance you will use the room. What is the expected value of your cost if you reserve the room with the flexible rate?
b. No longer assume a specific value for p. In terms of p, what is the expected value of your cost if you reserve the room with the flexible rate?
c. What is the expected value of your cost if you choose the advanced purchase rate?
d. For what value of p are the expected values you found in parts (b) and (c) the same?
e. For what range of values of p are you better off choosing the advanced purchase rate?