You are deciding whether to buy a lottery ticket for $5. The ticket gives a 1% chance of winning $500 and a 99% chance of winning nothing.

To determine whether buying the lottery ticket is a good decision, you can calculate the **expected value** of the ticket. The expected value helps to quantify the potential outcomes by considering both the probability of winning and the prize amount.

Here are the steps:

1. **Identify the probabilities and outcomes**:
   - Probability of winning ($500): 1% or 0.01.
   - Probability of winning nothing ($0): 99% or 0.99.
   - Cost of the ticket: $5.

2. **Calculate the expected value (EV)**:
   The expected value of the lottery ticket can be calculated using the formula:
   \[
   \text{EV} = (P(\text{win}) \times \text{Prize}) + (P(\text{lose}) \times \text{Lose})
   \]
   Substituting the values:
   \[
   \text{EV} = (0.01 \times 500) + (0.99 \times 0)
   \]
   \[
   \text{EV} = 5
   \]
   So, the expected value of the lottery ticket is **$5**.

3. **Compare the expected value to the ticket cost**:
   The expected value is $5, which is exactly the price of the ticket. In this case, on average, you would break even.

**Conclusion**:
Based on the expected value, this lottery ticket is neither a good nor a bad bet purely from a mathematical standpoint, as the expected value matches the cost. However, personal factors like risk tolerance or excitement might influence your decision.

Would you like further details or have any questions?

### Related questions:
1. How does expected value help in decision-making?
2. What is the difference between expected value and actual outcomes in probability?
3. How do risk and reward factor into gambling strategies?
4. What are other examples of expected value in real life?
5. How does variance affect lottery or gambling decisions?

**Tip**: Always compare the expected value to the cost to assess whether a gamble is worth it.

Learn how to calculate the expected value of a $5 lottery ticket with a 1% chance of winning $500. This example demonstrates probability and expected value concepts, perfect for high school students studying probability theory. Suitable for Grades 10-12.

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