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When playing roulette at a casino, a gambler is trying to decide whether to bet $15 on the number 30 or to bet $15 that the outcome is any one of the five possibilities 00, 0, 1, 2, or 3. The gambler knows that the 33 expected value of the $15 bet for a single number is -79¢. For the $15 bet that the outcome is 00, 0, 1, 2, or 3, there is a probability of 38 of making a net profit of $90 and a probability of losing $15. 38 a. Find the expected value for the $15 bet that the outcome is 00, 0, 1, 2, or 3. b. Which bet is better: a $15 bet on the number 30 or a $15 bet that the outcome is any one of the numbers 00, 0, 1, 2, or 3? Why? a. The expected value is $. (Round to the nearest cent as needed.) b. Since the expected value of the bet on the number 30 is ……… than the expected value for the bet that the outcome is 00, 0, 1, 2, or 3, the bet on ▼is better.

When playing roulette at a casino, a gambler is trying to decide whether to bet $15 on the number 30 or to bet $15 that the outcome is any one of the five possibilities 00, 0, 1, 2, or 3. The gambler knows that the 33 expected value of the $15 bet for a single number is -79¢. For the $15 bet that the outcome is 00, 0, 1, 2, or 3, there is a probability of 38 of making a net profit of $90 and a probability of losing $15. 38 a. Find the expected value for the $15 bet that the outcome is 00, 0, 1, 2, or 3. b. Which bet is better: a $15 bet on the number 30 or a $15 bet that the outcome is any one of the numbers 00, 0, 1, 2, or 3? Why? a. The expected value is $. (Round to the nearest cent as needed.) b. Since the expected value of the bet on the number 30 is ……… than the expected value for the bet that the outcome is 00, 0, 1, 2, or 3, the bet on ▼is better.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Educational Content on Expected Value and Probability in Roulette** **Understanding Roulette Betting Options** When playing roulette at a casino, a gambler faces the decision to place a $15 bet on the number 30 or to bet $15 that the outcome will be one of the five numbers: 00, 0, 1, 2, or 3. The gambler is aware of the following: 1. The expected value of a $15 bet on a single number is -$7.89. This indicates a likely loss over time if the gambles are repeated. 2. For the $15 bet that the outcome is one of the numbers 00, 0, 1, 2, or 3, the probability of achieving a net profit of $90 is \( \frac{5}{38} \). Conversely, there is a \( \frac{33}{38} \) probability of losing the $15 bet. **Task Breakdown** a. **Expected Value Calculation** - Calculate the expected value for the $15 bet that the outcome will be one of the numbers 00, 0, 1, 2, or 3. b. **Bet Comparison** - Compare the expected value of the bet on the number 30 to the expected value of the bet on the numbers 00, 0, 1, 2, or 3 to determine which bet is more advantageous. **Calculation Points** - **a.** Use the probabilities provided to calculate the expected gain or loss for the $15 bet on the numbers 00, 0, 1, 2, or 3. You'll need to weigh the potential profit against the probability of losing. - **b.** Analyze which bet has a higher expected value to decide the better option based on expected outcomes. While one bet may have a lower probability of winning, it may offer a higher expected return. This understanding helps illustrate the concept of expected value and decision-making in gambling, particularly in games of chance like roulette.
Transcribed Image Text:**Educational Content on Expected Value and Probability in Roulette** **Understanding Roulette Betting Options** When playing roulette at a casino, a gambler faces the decision to place a $15 bet on the number 30 or to bet $15 that the outcome will be one of the five numbers: 00, 0, 1, 2, or 3. The gambler is aware of the following: 1. The expected value of a $15 bet on a single number is -$7.89. This indicates a likely loss over time if the gambles are repeated. 2. For the $15 bet that the outcome is one of the numbers 00, 0, 1, 2, or 3, the probability of achieving a net profit of $90 is \( \frac{5}{38} \). Conversely, there is a \( \frac{33}{38} \) probability of losing the $15 bet. **Task Breakdown** a. **Expected Value Calculation** - Calculate the expected value for the $15 bet that the outcome will be one of the numbers 00, 0, 1, 2, or 3. b. **Bet Comparison** - Compare the expected value of the bet on the number 30 to the expected value of the bet on the numbers 00, 0, 1, 2, or 3 to determine which bet is more advantageous. **Calculation Points** - **a.** Use the probabilities provided to calculate the expected gain or loss for the $15 bet on the numbers 00, 0, 1, 2, or 3. You'll need to weigh the potential profit against the probability of losing. - **b.** Analyze which bet has a higher expected value to decide the better option based on expected outcomes. While one bet may have a lower probability of winning, it may offer a higher expected return. This understanding helps illustrate the concept of expected value and decision-making in gambling, particularly in games of chance like roulette.
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