Analyze decisions and strategies using probability concepts.
Example Problems
Bob's Bagel Shop has estimated the following probabilities for the number of bagels a randomly-selected customer buys when he or she enters the shop.
Bob sells bagels for each, or for a dozen. If is the amount of money Bob collects from a randomly-selected customer,
a. Find the expected value of .
b. Interpret the expected value of .
| No. of Bagels | Probability |
|---|---|
| 1 | 0.5 |
| 2 | 0.1 |
| 3 | 0.1 |
| 6 | 0.1 |
| 12 | 0.2 |
Bob sells bagels for each, or for a dozen. If is the amount of money Bob collects from a randomly-selected customer,
a. Find the expected value of .
b. Interpret the expected value of .
A friend of yours, Phil, writes to you asking about a new scratch-off lottery game. It costs to play this game. There are two outcomes for the game (win, lose) and the probability that a player wins a game is . A win results in , for a net win of .
The probability distribution for , the amount of money a player wins (or loses) in a single game, is as follows:
a. Compute the expected value of .
b. Your friend wants to know if he should play this game many, many times to make some extra money because the chance of winning sounds really good. Based on your calculation in part (a), complete the following message to your friend Phil that clearly recommends whether or not he should play this game many, many times and explains how the value you computed in part (a) led you to that conclusion.
Phil:
Regarding your idea that you should play this new lottery game many, many times to make some extra money, I think...
The probability distribution for , the amount of money a player wins (or loses) in a single game, is as follows:
| Probability of | |
|---|---|
a. Compute the expected value of .
b. Your friend wants to know if he should play this game many, many times to make some extra money because the chance of winning sounds really good. Based on your calculation in part (a), complete the following message to your friend Phil that clearly recommends whether or not he should play this game many, many times and explains how the value you computed in part (a) led you to that conclusion.
Phil:
Regarding your idea that you should play this new lottery game many, many times to make some extra money, I think...
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