To determine the expected value of the lottery ticket, we use the following formula:

$\text{Expected Value} = ( \text{Prize} \times \text{Probability of Winning} )$

Given:

• Prize = $30.8 million
• Probability of winning = 0.000000050

Calculating the expected value:

$\text{Expected Value} = 30,800,000 \times 0.000000050$

$\text{Expected Value} = 1.54$

The expected value of the lottery ticket is $1.54.

To check if paying $1 for a ticket is greater than the expected winnings:

• Expected value = $1.54
• Cost of ticket = $1

Since $1.54 (expected winnings) is greater than $1 (cost of ticket), the answer is "No," paying $1 for a ticket is not greater than the expected winnings.

Would you like any further details or have any questions?

Here are some related questions for further exploration:

1. How does the expected value change if the prize amount increases?
2. What happens to the expected value if the probability of winning decreases?
3. How would the expected value be affected if the prize amount was $50 million?
4. What is the expected value if the probability of winning is doubled?
5. How do you calculate the variance and standard deviation for lottery winnings?
6. How does the cost of the lottery ticket affect the decision to purchase it based on expected value?
7. What are the implications of expected value in making gambling decisions?
8. Can expected value calculations be applied to other forms of gambling?

Tip: When calculating expected values, always ensure that the probability and prize values are correctly identified and input into the formula.