**Expected Value in a Roulette Bet on Black**In a popular casino game, you can bet on whether a ball will land in an arc on a wheel colored red, black, or green. The probability of different outcomes is given as follows:- Probability of a red outcome: $ \frac{18}{38} $- Probability of a black outcome: $ \frac{18}{38} $- Probability of a green outcome: $ \frac{2}{38} $Suppose someone makes a $5 bet on black. Find the expected net winnings for this single bet and interpret the result.**Question**:Choose the correct answer below and fill in the answer box to complete your choice. (Round to three decimal places as needed.)**Options**:- **A.** If the $5 bet on black was placed a very large number of times, the bettor would win a total of $\underline{\hspace{1cm}}$ dollars.- **B.** A person will win $\underline{\hspace{1cm}}$ dollars every time a $5 bet was placed on black.- **C.** On average, a person is expected to win $\underline{\hspace{1cm}}$ dollars for any bet on the roulette wheel.- **D.** If the $5 bet on black was placed a very large number of times, the average winnings would be $\underline{\hspace{1cm}}$ dollars per bet.To find the expected net winnings, we will calculate the expected value (EV) for the bet.**Calculation**:1. **Net gain if black wins**: The bettor wins $5 and keeps the $5 bet, resulting in a net gain of $5.2. **Net loss if black loses**: The bettor loses the $5 bet.3. **Probability of winning**: $ \frac{18}{38} $4. **Probability of losing**: $ 1 - \frac{18}{38} = \frac{20}{38} $**Expected Value (EV)**:- EV = (Net gain) \* (Probability of winning) + (Net loss) \* (Probability of losing)- EV = ($5) \* $ \frac{18}{38} $ + (-$5) \* $ \frac{20}{38} $- EV = $5 \

Name: **Expected Value in a Roulette Bet on Black**In a popular casino game
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Description: **Expected Value in a Roulette Bet on Black**In a popular casino game, you can bet on whether a ball will land in an arc on a wheel colored red, black, or green. The probability of different outcomes is given as follows:- Probability of a red outcom

To find: The expected net winnings for the single bet.

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Question Help ▼ 18 In a popular casino game, you can bet one whether a ball will fall in an arc on a wheel colored red, black, or green. Say the probability of a red outcome is 38 18 that of a black outcome is , and that of a green outcome is . Suppose someone makes a $5 bet on black. Find the expected net winnings for this single bet. Interpret the result. Choose the correct answer below and fill in the answer box to complete your choice. (Round to three decimal places as needed.) O A. If the $5 bet on black was placed a very large number of times, the bettor would win a total of dollars O B. A person will win dollars every time a $5 bet was placed on black. O C. On average, a person is expected to win dollars for any bet on the roulette wheel. O D. If the $5 bet on black was placed a very large number of times, the average winnings would be dollars per bet.

Question Help ▼ 18 In a popular casino game, you can bet one whether a ball will fall in an arc on a wheel colored red, black, or green. Say the probability of a red outcome is 38 18 that of a black outcome is , and that of a green outcome is . Suppose someone makes a $5 bet on black. Find the expected net winnings for this single bet. Interpret the result. Choose the correct answer below and fill in the answer box to complete your choice. (Round to three decimal places as needed.) O A. If the $5 bet on black was placed a very large number of times, the bettor would win a total of dollars O B. A person will win dollars every time a $5 bet was placed on black. O C. On average, a person is expected to win dollars for any bet on the roulette wheel. O D. If the $5 bet on black was placed a very large number of times, the average winnings would be dollars per bet.

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

**Expected Value in a Roulette Bet on Black**

In a popular casino game, you can bet on whether a ball will land in an arc on a wheel colored red, black, or green. The probability of different outcomes is given as follows:
- Probability of a red outcome: $ \frac{18}{38} $
- Probability of a black outcome: $ \frac{18}{38} $
- Probability of a green outcome: $ \frac{2}{38} $

Suppose someone makes a $5 bet on black. Find the expected net winnings for this single bet and interpret the result.

**Question**:
Choose the correct answer below and fill in the answer box to complete your choice. (Round to three decimal places as needed.)

**Options**:
- **A.** If the $5 bet on black was placed a very large number of times, the bettor would win a total of $\underline{\hspace{1cm}}$ dollars.
- **B.** A person will win $\underline{\hspace{1cm}}$ dollars every time a $5 bet was placed on black.
- **C.** On average, a person is expected to win $\underline{\hspace{1cm}}$ dollars for any bet on the roulette wheel.
- **D.** If the $5 bet on black was placed a very large number of times, the average winnings would be $\underline{\hspace{1cm}}$ dollars per bet.

To find the expected net winnings, we will calculate the expected value (EV) for the bet.

**Calculation**:

1. **Net gain if black wins**: The bettor wins $5 and keeps the $5 bet, resulting in a net gain of $5.
2. **Net loss if black loses**: The bettor loses the $5 bet.
3. **Probability of winning**: $ \frac{18}{38} $
4. **Probability of losing**: $ 1 - \frac{18}{38} = \frac{20}{38} $

**Expected Value (EV)**:
- EV = (Net gain) \* (Probability of winning) + (Net loss) \* (Probability of losing)
- EV = ($5) \* $ \frac{18}{38} $ + (-$5) \* $ \frac{20}{38} $
- EV = $5 \

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In a popular casino game, you can bet one whether a ball will fall in an arc on a wheel colored red, black, or green. Say the probability of a red outcome is 18 that of a black outcome is 36, and that of a green outcome is 2 Suppose someone makes a S25 bet on black. Find the expected net winnings for this single bet. Interpret the result. Choose the correct answer below and fill in the answer box to complete your choice. (Round to three decimal places as needed.) O A. If the $25 bet on black was placed a very large number of times, the bettor would win a total of dollars. O B. If the $25 bet on black was placed a very large number of times, the average winnings would be dollars per bet. O C. On average, a person is expected to win dollars for any bet on the roulette wheel. OD. A person will win dollars every time a $25 bet was placed on black.