A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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![**Title:** Understanding Expected Value in Slot Machines
**Text:**
Let's say you own a slot machine with a 1 out of 88 chance of a 269 prize. What do you need to charge to break even?
*Hint: what is the expected value?*
**Explanation:**
This exercise introduces the concept of expected value, a fundamental principle in probability and finance. In this scenario, the expected value represents the average amount a slot owner would receive per play in the long run, allowing them to break even on costs over time.
To calculate the expected value:
1. Multiply the probability of winning by the prize amount:
\[ \text{Expected Value} = \left(\frac{1}{88}\right) \times 269 \]
2. The result will give the average amount that should be charged per play to ensure no loss or gain from the slot machine over multiple plays. This helps the owner set a price that offsets the payout risk.](https://content.bartleby.com/qna-images/question/d47d2725-9ed4-4a07-8ea4-b309d33139a1/aa8bb511-f755-40ce-9e13-ad38664e58d4/2fduqc_processed.jpeg)
Transcribed Image Text:**Title:** Understanding Expected Value in Slot Machines
**Text:**
Let's say you own a slot machine with a 1 out of 88 chance of a 269 prize. What do you need to charge to break even?
*Hint: what is the expected value?*
**Explanation:**
This exercise introduces the concept of expected value, a fundamental principle in probability and finance. In this scenario, the expected value represents the average amount a slot owner would receive per play in the long run, allowing them to break even on costs over time.
To calculate the expected value:
1. Multiply the probability of winning by the prize amount:
\[ \text{Expected Value} = \left(\frac{1}{88}\right) \times 269 \]
2. The result will give the average amount that should be charged per play to ensure no loss or gain from the slot machine over multiple plays. This helps the owner set a price that offsets the payout risk.
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