You buy a lottery ticket to a lottery that cost $10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $500 prize, two $100 prizes, and four $25 prizes. Find your expected gain or loss. Do you still want to play raffle?

plug into calculator.

L1 L2
-10 93/100
499 1/100
99 2/100
24 4/100

STAT- CALU-#1:1-VAR STATS-ENTER-2ND #1(L1), THEN "," THEN 2ND #2(L2)-ENTER

YOUR FIRST X AT THE TOP IS YOUR EXPECTATION OR MEAN.

To find your expected gain or loss in the lottery, we need to calculate the probability of winning each prize and multiply it by the amount you can win.

Let's start with the $500 prize. Since there's only one $500 prize and 100 tickets sold, the probability of winning the $500 prize is 1/100.

Next, we have the two $100 prizes. The probability of winning the first $100 prize is 1/100, and the probability of winning the second $100 prize is 1/99 (as one ticket has already been drawn). So, the total probability of winning a $100 prize is (1/100) + (1/99).

Finally, we have the four $25 prizes. Similarly, the probability of winning the first $25 prize is 1/100, the probability of winning the second $25 prize is 1/99, the probability of winning the third $25 prize is 1/98, and the probability of winning the fourth $25 prize is 1/97. So, the total probability of winning a $25 prize is (1/100) + (1/99) + (1/98) + (1/97).

To calculate the expected gain or loss, we multiply each probability by the corresponding amount you can win and sum them up:

Expected Gain = (1/100) * $500 + (1/100 + 1/99) * $100 + (1/100 + 1/99 + 1/98 + 1/97) * $25

Now, let's evaluate this expression:

Expected Gain = (1/100) * $500 + (1/100 + 1/99) * $100 + (1/100 + 1/99 + 1/98 + 1/97) * $25
Expected Gain ≈ $5 + $2.02 + $1.08
Expected Gain ≈ $8.10

Therefore, your expected gain in this lottery is $8.10. This means, on average, you can expect to win $8.10 per ticket played.

Considering that each ticket costs $10, the expected loss is $10 - $8.10 = $1.90 per ticket played.

Based on the expected gain/loss, it seems that, on average, you may lose money by playing this lottery. Hence, it might not be the most profitable choice.

To calculate the expected gain or loss, we need to consider the probability of winning each prize. Let's calculate it step-by-step:

Step 1: Calculate the total amount of money paid in by all participants.
Total amount paid in = Number of tickets sold * Cost per ticket
Total amount paid in = 100 tickets * $10 per ticket
Total amount paid in = $1000

Step 2: Calculate the probability of winning each prize.
Probability of winning $500 prize = 1/100 = 0.01 or 1%
Probability of winning $100 prize = 2/100 = 0.02 or 2%
Probability of winning $25 prize = 4/100 = 0.04 or 4%

Step 3: Calculate the expected gain or loss.
Expected gain or loss = (Probability of winning $500 prize * $500) + (Probability of winning $100 prize * $100) + (Probability of winning $25 prize * $25) - Total amount paid in
Expected gain or loss = (0.01 * $500) + (0.02 * $100) + (0.04 * $25) - $1000
Expected gain or loss = $5 + $2 + $1 - $1000
Expected gain or loss = $8 - $1000
Expected gain or loss = -$992 (a loss of $992)

Based on the calculation, the expected gain or loss is a significant loss of $992. It's not advisable to play the raffle as the expected outcome suggests a large negative return on investment.