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When playing roulette at a casino, a gambler is trying to decide whether to bet $5 on the number 25 or to bet $5 that the outcome is any one of the three possibilities 00, 0, or 1. The gambler knows that the expected value of the $5 bet 3 for a single number is - 26¢. For the $5 bet that the outcome is 00, 0, or 1, there is a probability of of making a 38 35 net profit of $15 and a probability of losing $5. 38 a. Find the expected value for the $5 bet that the outcome is 00, 0, or 1. b. Which bet is better: a $5 bet on the number 25 or a $5 bet that the outcome is any one of the numbers 00, 0, or 1? Why? a. The expected value is $ (Round to the nearest cent as needed.)

When playing roulette at a casino, a gambler is trying to decide whether to bet $5 on the number 25 or to bet $5 that the outcome is any one of the three possibilities 00, 0, or 1. The gambler knows that the expected value of the $5 bet 3 for a single number is - 26¢. For the $5 bet that the outcome is 00, 0, or 1, there is a probability of of making a 38 35 net profit of $15 and a probability of losing $5. 38 a. Find the expected value for the $5 bet that the outcome is 00, 0, or 1. b. Which bet is better: a $5 bet on the number 25 or a $5 bet that the outcome is any one of the numbers 00, 0, or 1? Why? a. The expected value is $ (Round to the nearest cent as needed.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Roulette Betting Strategy: Analyzing Expected Values** In a roulette game, a gambler is considering two betting options. One option is to place a $5 bet on the number 25, while the other option is to bet $5 that the outcome is either 00, 0, or 1. **Known Information:** - The expected value of a $5 bet on any single number is -26 cents. - If the outcome is 00, 0, or 1, a $5 bet results in a net profit of $15. - There is a probability of \( \frac{3}{38} \) of the outcome being 00, 0, or 1. - The probability of losing the $5 is \( \frac{35}{38} \). **Tasks:** a. Determine the expected value for the $5 bet on the outcome being 00, 0, or 1. b. Evaluate which option is preferable: the $5 bet on the number 25 or on the numbers 00, 0, or 1. Provide reasoning for the choice. **Solution:** a. The expected value for the $5 bet when the outcome is 00, 0, or 1 is calculated by considering the probabilities and potential outcomes: Given: - Probability of winning $15: \( \frac{3}{38} \) - Probability of losing $5: \( \frac{35}{38} \) Expected Value (EV) = \( \left(\frac{3}{38} \times 15\right) + \left(\frac{35}{38} \times (-5)\right) = \) ____ (Round to the nearest cent as necessary) b. Compare the calculated expected value for the $5 bet on 00, 0, or 1 with the known expected value of -26 cents for the single number bet. Decide which bet is better based on the expected values.
Transcribed Image Text:**Roulette Betting Strategy: Analyzing Expected Values** In a roulette game, a gambler is considering two betting options. One option is to place a $5 bet on the number 25, while the other option is to bet $5 that the outcome is either 00, 0, or 1. **Known Information:** - The expected value of a $5 bet on any single number is -26 cents. - If the outcome is 00, 0, or 1, a $5 bet results in a net profit of $15. - There is a probability of \( \frac{3}{38} \) of the outcome being 00, 0, or 1. - The probability of losing the $5 is \( \frac{35}{38} \). **Tasks:** a. Determine the expected value for the $5 bet on the outcome being 00, 0, or 1. b. Evaluate which option is preferable: the $5 bet on the number 25 or on the numbers 00, 0, or 1. Provide reasoning for the choice. **Solution:** a. The expected value for the $5 bet when the outcome is 00, 0, or 1 is calculated by considering the probabilities and potential outcomes: Given: - Probability of winning $15: \( \frac{3}{38} \) - Probability of losing $5: \( \frac{35}{38} \) Expected Value (EV) = \( \left(\frac{3}{38} \times 15\right) + \left(\frac{35}{38} \times (-5)\right) = \) ____ (Round to the nearest cent as necessary) b. Compare the calculated expected value for the $5 bet on 00, 0, or 1 with the known expected value of -26 cents for the single number bet. Decide which bet is better based on the expected values.
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