https://r2.erweima.ai/mathbot/image/1727231182486kq5ttsvl.jpg

To find the expected value for each raffle ticket bought, we need to calculate the total expected value based on the given prizes and their associated probabilities.

We are given the following information from the table:

1. **First Prize**: $35, with a probability of $\frac{2}{350}$.
2. **Second Prize**: $7, with a probability of $\frac{5}{350}$.
3. **Third Prize**: $4, with a probability of $\frac{8}{350}$.

### Step 1: Calculate the expected value from the prizes (without subtracting the ticket cost).

The expected value is calculated by multiplying each prize by its probability and summing up the results:

\[
\text{Expected Value} = \left( 35 \times \frac{2}{350} \right) + \left( 7 \times \frac{5}{350} \right) + \left( 4 \times \frac{8}{350} \right)
\]

Let me calculate this for you.The expected value of the raffle prize, before accounting for the cost of the ticket, is approximately **$0.39**.

### Step 2: Subtract the cost of the ticket.

Each ticket costs $2, so to find the net expected value for each ticket bought, we subtract the ticket cost from the expected value:

\[
\text{Net Expected Value} = 0.39 - 2 = -1.61
\]

Thus, the net expected value of each ticket is **-$1.61**. This means that, on average, a person will lose $1.61 per ticket purchased.

Would you like more details or further explanation?

Here are 5 related questions:
1. What if the cost of each ticket was $1 instead of $2?
2. How would the expected value change if there were more prizes?
3. What does a negative expected value mean in this context?
4. How would increasing the number of high-value prizes affect the expected value?
5. Can you calculate the probability of not winning anything?

**Tip**: A negative expected value suggests that, on average, participants are likely to lose money.

What is the expected value for each of these tickets bought?

Learn how to calculate the expected value of raffle tickets using the probabilities of winning different prizes. This problem explores core concepts of probability and expected value, appropriate for Grades 9-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation