At a​ raffle, 10,000 tickets are sold at​ $5 each for three prizes valued at​ $4,800, $1,200, and​ $400. What is the expected value of one​ ticket?

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Part 1

A.

minus−​$4.36

B.

​$4.36

C.

​$0.64

D.

minus−​$0.64

To calculate the expected value of one raffle ticket, we'll consider both the probability of winning each prize and the probability of not winning anything.

### Step 1: Calculate the probability of winning each prize.
- **Total number of tickets:** 10,000
- **Prize 1 value:** $4,800 (1 ticket wins)
- **Prize 2 value:** $1,200 (1 ticket wins)
- **Prize 3 value:** $400 (1 ticket wins)

**Probability of winning each prize:**
- Probability of winning the $4,800 prize: $ \frac{1}{10{,}000} $
- Probability of winning the $1,200 prize: $ \frac{1}{10{,}000} $
- Probability of winning the $400 prize: $ \frac{1}{10{,}000} $

### Step 2: Calculate the expected value from each prize.
- **Expected value from Prize 1:** $ \frac{1}{10{,}000} \times 4{,}800 = 0.48 $
- **Expected value from Prize 2:** $ \frac{1}{10{,}000} \times 1{,}200 = 0.12 $
- **Expected value from Prize 3:** $ \frac{1}{10{,}000} \times 400 = 0.04 $

### Step 3: Calculate the total expected value of winning.
- **Total expected value of winning:** $ 0.48 + 0.12 + 0.04 = 0.64 $

### Step 4: Calculate the expected value after subtracting the cost of the ticket.
- **Cost of ticket:** $5.00
- **Net expected value:** $ 0.64 - 5.00 = -4.36 $

Thus, the expected value of one ticket is $-\$4.36$.

### Final Answer:
**A. $-\$4.36$**

Would you like details or have any questions?

Here are 5 related questions:
1. How would the expected value change if more tickets were sold?
2. What is the expected value if the ticket price was reduced to $3?
3. How does the expected value compare to simply investing $5 in a savings account?
4. What is the probability of winning at least one of the prizes?
5. How would the expected value change if the value of the prizes were increased?

**Tip:** Understanding expected value can help in making informed decisions about participating in lotteries and raffles.

At a raffle, 10,000 tickets are sold at $5 each for three prizes valued at $4,800, $1,200, and $400. What is the expected value of one ticket?

Learn how to calculate the expected value of a raffle ticket in a scenario where 10,000 tickets are sold, and prizes worth $4,800, $1,200, and $400 are awarded. Understand key concepts such as probability and cost-benefit analysis. Suitable for high school students (Grades 9-12).

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