Lottery: In the New York State Numbers lottery, you pay $3 and can bet that the sum of the numbers that come up is 13. The probability of winning is 0.07, and if you win, you win $6, which is a profit of $3. If you lose, you lose $3. Part: 0/2 Part 1 of 2 (a) What is the expected value of your profit? Round the answer to two decimal places. The expected value of profit is X
Lottery: In the New York State Numbers lottery, you pay $3 and can bet that the sum of the numbers that come up is 13. The probability of winning is 0.07, and if you win, you win $6, which is a profit of $3. If you lose, you lose $3. Part: 0/2 Part 1 of 2 (a) What is the expected value of your profit? Round the answer to two decimal places. The expected value of profit is X
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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![### Lottery Exercise
#### Instructions:
In the New York State Numbers lottery, you pay $3 and can bet that the sum of the numbers that come up is 13. If you win, you win $5, which is a profit of $3. If you lose, you lose $3.
#### Questions:
##### Part 1 of 2:
(a) What is the expected value of your profit? Round the answer to two decimal places.
- The expected value of profit is: \[\_\_\_\_\_]
#### Submission Options:
- **Skip Part**: Skip and move to the next part of the question.
- **Check**: Verify the entered answer for correctness.
- **Save For Later**: Save your progress to return to the question later.
- **Submit Assignment**: Submit the assignment for evaluation.
#### Navigation:
- Use the buttons provided to navigate through the exercise and manage your progress and submissions.
### Example Calculation:
To calculate the expected value of profit, use the following steps:
1. Determine the profit for winning and losing.
2. Multiply each profit by its respective probability.
3. Sum these values to find the expected value.
Given:
- Cost of playing: $3
- Winning amount: $5
- Net profit if win: $5 - $3 = $2
- Net profit if lose: -$3
- Probability of winning: 0.017
- Probability of losing: 1 - 0.017 = 0.983
Expected Value Calculation:
\[ E(X) = (2 \times 0.017) + (-3 \times 0.983) \]
Understanding this concept will help in making informed decisions about participating in such lotteries.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29a07bd8-eb1c-498d-b0a8-9eb9d6fddf09%2F44a114b1-cf3f-468c-b1f3-bf808593d9ac%2F9g1xsd9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Lottery Exercise
#### Instructions:
In the New York State Numbers lottery, you pay $3 and can bet that the sum of the numbers that come up is 13. If you win, you win $5, which is a profit of $3. If you lose, you lose $3.
#### Questions:
##### Part 1 of 2:
(a) What is the expected value of your profit? Round the answer to two decimal places.
- The expected value of profit is: \[\_\_\_\_\_]
#### Submission Options:
- **Skip Part**: Skip and move to the next part of the question.
- **Check**: Verify the entered answer for correctness.
- **Save For Later**: Save your progress to return to the question later.
- **Submit Assignment**: Submit the assignment for evaluation.
#### Navigation:
- Use the buttons provided to navigate through the exercise and manage your progress and submissions.
### Example Calculation:
To calculate the expected value of profit, use the following steps:
1. Determine the profit for winning and losing.
2. Multiply each profit by its respective probability.
3. Sum these values to find the expected value.
Given:
- Cost of playing: $3
- Winning amount: $5
- Net profit if win: $5 - $3 = $2
- Net profit if lose: -$3
- Probability of winning: 0.017
- Probability of losing: 1 - 0.017 = 0.983
Expected Value Calculation:
\[ E(X) = (2 \times 0.017) + (-3 \times 0.983) \]
Understanding this concept will help in making informed decisions about participating in such lotteries.
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