A scratch off lottery ticket can be purchased for  
$
2
 . There are multiple prize options, shown along with the probability, in the table below. What is the expected win (or loss) for this lottery ticket?

Round your answer to the nearest cent. Do not round until your final answer.

Win	Probability
$
5
,
000
 	 
0.000125
 
$
250
 	 
0.000375
 
$
75
 	 
0.002
 
$
10
 	 
0.0025
 
$
2
 	 
0.02
 
0
 	 
0.975
 
 

To calculate the expected win or loss, we'll need to compute the expected value of the lottery ticket. The expected value (EV) is the sum of all possible outcomes, weighted by their probabilities. 

The formula for expected value is:

\[
EV = \sum (\text{{win amount}} \times \text{{probability}})
\]

We'll compute the expected winnings for each prize, then subtract the cost of the ticket ($2) from the result to find the expected profit or loss.

### Given:
- Win amounts and their probabilities are provided in the table:
  
  \[
  \begin{aligned}
  &5000: 0.000125 \\
  &250: 0.000375 \\
  &75: 0.002 \\
  &10: 0.0025 \\
  &2: 0.02 \\
  &0: 0.975
  \end{aligned}
  \]

Let's compute the expected value of the winnings.The expected net loss for this lottery ticket is approximately $-$$1.07. This means that on average, you lose $1.07 each time you purchase a ticket.

Would you like further details or have any questions? 

Here are 5 related questions for further exploration:

1. How is expected value used in other gambling scenarios?
2. How would the result change if the ticket cost increased?
3. What is the variance in lottery winnings, and how does it affect risk?
4. What is the probability of at least breaking even with this ticket?
5. How does expected value compare to median or mode in lotteries?

**Tip:** The expected value helps assess long-term outcomes but doesn't predict individual results.

A scratch off lottery ticket can be purchased for $2. There are multiple prize options, shown along with the probability, in the table below. What is the expected win (or loss) for this lottery ticket? Round your answer to the nearest cent. Do not round until your final answer. Win Probability $5,000 0.000125 $250 0.000375 $75 0.002 $10 0.0025 $2 0.02 0 0.975

Learn how to calculate the expected win or loss for a $2 scratch off lottery ticket. This problem involves key probability concepts and uses the expected value formula to find the expected outcome. Explore detailed calculations for multiple prize options, including $5,000, $250, and more. Suitable for high school students (Grades 9-12).

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