The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $10 each and will sell 700 tickets. There is one $2,000 grand prize, three $300 second prizes, and twelve $30 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.
The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $10 each and will sell 700 tickets. There is one $2,000 grand prize, three $300 second prizes, and twelve $30 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.
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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**Explanation:**
The problem presents a scenario where you need to calculate the expected value of your profit when you buy a ticket in a drawing. The calculation involves understanding the probabilities and potential outcomes:
- 1 ticket out of 700 wins the $2,000 grand prize.
- 3 tickets out of 700 win the $300 second prize.
- 12 tickets out of 700 win the $30 third prize.
The expected value is calculated as the sum of each possible outcome weighted by its probability. You would subtract the cost of the ticket ($10) from each prize to get the net outcomes before multiplying by the respective probabilities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77379e33-cd78-4bf1-a88e-5489bb4fa9c3%2F3f4a3ffb-cba4-446f-8d36-22e3da22a9a9%2Ffah2x1g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $10 each and will sell 700 tickets. There is one $2,000 grand prize, three $300 second prizes, and twelve $30 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.
**Answer Box:**
```
$_____
```
**Hints and Resources:**
- [Hint](#)
- [Video on Expected Value](#)
**Action Button:**
- [Submit Question](#)
**Explanation:**
The problem presents a scenario where you need to calculate the expected value of your profit when you buy a ticket in a drawing. The calculation involves understanding the probabilities and potential outcomes:
- 1 ticket out of 700 wins the $2,000 grand prize.
- 3 tickets out of 700 win the $300 second prize.
- 12 tickets out of 700 win the $30 third prize.
The expected value is calculated as the sum of each possible outcome weighted by its probability. You would subtract the cost of the ticket ($10) from each prize to get the net outcomes before multiplying by the respective probabilities.
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