The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $9 each and will sell 600 tickets. There is one $3,000 grand prize, four $200 second prizes, and sixteen $40 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 $9 each and will sell 600 tickets. There is one $3,000 grand prize, four $200 second prizes, and sixteen $40 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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![#### Fundraising Raffle Probability Calculation
The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $9 each and will sell 600 tickets.
**Prize details:**
- One grand prize of $3,000
- Four second prizes of $200 each
- Sixteen third prizes of $40 each
You have purchased a ticket for this drawing.
**Task:**
Find the expected value for your profit. Round to the nearest cent.
\[ \text{Expected Value (EV)} = \$ \text{input box} \]
**Steps to calculate the expected value:**
1. **Determine the probability of each event:**
- Probability of winning the grand prize: \(\frac{1}{600}\)
- Probability of winning a second prize: \(\frac{4}{600}\)
- Probability of winning a third prize: \(\frac{16}{600}\)
- Probability of not winning any prize: \(\frac{579}{600}\)
2. **Calculate the net winnings for each event:**
- Grand prize net winnings: \(\$3000 - \$9 = \$2991\)
- Second prize net winnings: \(\$200 - \$9 = \$191\)
- Third prize net winnings: \(\$40 - \$9 = \$31\)
- No prize net loss: \(-\$9\)
3. **Multiply each net winning by its corresponding probability and sum these values to find the expected value:**
\[ \text{Expected Value} = (2991 \times \frac{1}{600}) + (191 \times \frac{4}{600}) + (31 \times \frac{16}{600}) + (-9 \times \frac{579}{600}) \]
\[ \text{Expected Value} = \left(\frac{2991}{600}\right) + \left(\frac{764}{600}\right) + \left(\frac{496}{600}\right) + \left(\frac{-5211}{600}\right) \]
\[ \text{Expected Value} = 4.985 + 1.2733 + 0.8267 - 8.685 \]
\[ \text{Expected Value} = -1.6 \]
Therefore, the expected value for your profit is \(-\$1.60\).
\[ -\$](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ccfad45-ecac-4aff-ad59-0890596e1f26%2F4c7d66fe-babd-4531-94c6-a118873801a9%2F0w7ufne_processed.jpeg&w=3840&q=75)
Transcribed Image Text:#### Fundraising Raffle Probability Calculation
The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $9 each and will sell 600 tickets.
**Prize details:**
- One grand prize of $3,000
- Four second prizes of $200 each
- Sixteen third prizes of $40 each
You have purchased a ticket for this drawing.
**Task:**
Find the expected value for your profit. Round to the nearest cent.
\[ \text{Expected Value (EV)} = \$ \text{input box} \]
**Steps to calculate the expected value:**
1. **Determine the probability of each event:**
- Probability of winning the grand prize: \(\frac{1}{600}\)
- Probability of winning a second prize: \(\frac{4}{600}\)
- Probability of winning a third prize: \(\frac{16}{600}\)
- Probability of not winning any prize: \(\frac{579}{600}\)
2. **Calculate the net winnings for each event:**
- Grand prize net winnings: \(\$3000 - \$9 = \$2991\)
- Second prize net winnings: \(\$200 - \$9 = \$191\)
- Third prize net winnings: \(\$40 - \$9 = \$31\)
- No prize net loss: \(-\$9\)
3. **Multiply each net winning by its corresponding probability and sum these values to find the expected value:**
\[ \text{Expected Value} = (2991 \times \frac{1}{600}) + (191 \times \frac{4}{600}) + (31 \times \frac{16}{600}) + (-9 \times \frac{579}{600}) \]
\[ \text{Expected Value} = \left(\frac{2991}{600}\right) + \left(\frac{764}{600}\right) + \left(\frac{496}{600}\right) + \left(\frac{-5211}{600}\right) \]
\[ \text{Expected Value} = 4.985 + 1.2733 + 0.8267 - 8.685 \]
\[ \text{Expected Value} = -1.6 \]
Therefore, the expected value for your profit is \(-\$1.60\).
\[ -\$
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