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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)
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.
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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