**Problem Statement:**A ping pong ball is drawn at random from an urn consisting of balls numbered 4 through 9. A player wins $1.5 if the number on the ball is odd and loses $1 if the number is even.Let $ x $ be the amount of money a player will win/lose when playing this game, where $ x $ is negative when the player loses money.**Tasks:**(a) Construct the probability distribution table for this game. Round your answers to two decimal places.| Outcome | $ x $ | Probability P(x) ||---------|--------|-------------------|| | | || | | || | | || | | || | | || | | |(b) What is the expected value of the player's winnings? Round to the nearest hundredth.\[ E(x) = \](c) Interpret the meaning of the expected value in the context of this problem.\[ \text{Interpretation:} \]**Explanation of the Diagram:**There are no graphs or diagrams included in the provided image. The image contains a problem statement involving the calculation of probabilities and an expected value, a layout for constructing a probability distribution table, and spaces for calculating and interpreting the expected value.---### Explanation:1. **Probability Distribution Table:** - **Possible Outcomes:** The outcomes depend on whether the ball drawn has an even or odd number. - **Amount Won/Lost (x):** Player wins $1.5 for odd numbers (5, 7, 9) and loses $1 for even numbers (4, 6, 8). - **Probability P(x):** Since the numbers 4 through 9 are equally likely, each has a probability of $\frac{1}{6}$.2. **Expected Value Calculation:** The expected value $ E(x) $ is calculated by multiplying each outcome $ x $ by its corresponding probability P(x) and summing these products.3. **Interpretation:** The expected value gives the average amount a player can expect to win or lose per game over a large number of trials. ### Filling in the Table: - For the numbers 5, 7, 9: Winners - $ x = 1.5 $ - Probability

Name: **Problem Statement:**A ping pong ball is drawn at random from an urn
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Description: **Problem Statement:**A ping pong ball is drawn at random from an urn consisting of balls numbered 4 through 9. A player wins $1.5 if the number on the ball is odd and loses $1 if the number is even.Let $ x $ be the amount of money a player will w

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A ping pong ball is drawn at random from an urn consisting of balls numbered 4 through 9. A player wins $1.5 if the number on the ball is odd and loses $1 if the number is even. Let x be the amount of money a player will win/lose when playing this game, where x is negative when the player loses money. (a) Construct the probability distribution table for this game. Round your answers to two decimal places. Probability P(x) Outcome

A ping pong ball is drawn at random from an urn consisting of balls numbered 4 through 9. A player wins $1.5 if the number on the ball is odd and loses $1 if the number is even. Let x be the amount of money a player will win/lose when playing this game, where x is negative when the player loses money. (a) Construct the probability distribution table for this game. Round your answers to two decimal places. Probability P(x) Outcome

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

**Problem Statement:**

A ping pong ball is drawn at random from an urn consisting of balls numbered 4 through 9. A player wins $1.5 if the number on the ball is odd and loses $1 if the number is even.

Let $ x $ be the amount of money a player will win/lose when playing this game, where $ x $ is negative when the player loses money.

**Tasks:**

(a) Construct the probability distribution table for this game. Round your answers to two decimal places.

| Outcome | $ x $ | Probability P(x) |
|---------|--------|-------------------|
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |

(b) What is the expected value of the player's winnings? Round to the nearest hundredth.

\[ E(x) = \]

(c) Interpret the meaning of the expected value in the context of this problem.

\[ \text{Interpretation:} \]

**Explanation of the Diagram:**

There are no graphs or diagrams included in the provided image. The image contains a problem statement involving the calculation of probabilities and an expected value, a layout for constructing a probability distribution table, and spaces for calculating and interpreting the expected value.

---

### Explanation:

1. **Probability Distribution Table:**

- **Possible Outcomes:** The outcomes depend on whether the ball drawn has an even or odd number.
- **Amount Won/Lost (x):** Player wins $1.5 for odd numbers (5, 7, 9) and loses $1 for even numbers (4, 6, 8).
- **Probability P(x):** Since the numbers 4 through 9 are equally likely, each has a probability of $\frac{1}{6}$.

2. **Expected Value Calculation:**

The expected value $ E(x) $ is calculated by multiplying each outcome $ x $ by its corresponding probability P(x) and summing these products.

3. **Interpretation:**

The expected value gives the average amount a player can expect to win or lose per game over a large number of trials.

### Filling in the Table:

- For the numbers 5, 7, 9: Winners
- $ x = 1.5 $
- Probability

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