Expected Net Winnings from 1,000 Raffle Tickets

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In summary, the problem involves the sale of 1,000 raffle tickets for $100 each with a winning prize worth $75,000. The expected net winnings for the winner can be calculated by subtracting the probability of losing ($100) from the probability of winning ($75,000) and multiplying it by the respective probabilities (1/1000 and 999/1000). The answer is -$25, meaning that on average, the winner will lose $25 on a $100 bet.
  • #1
sdlisa
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Homework Statement


1,000 raffle tickets are being sold for $100 each. The winning prize is worth $75,000. Find the expected net winnign for the winner if he/she buys one ticket.


Homework Equations





The Attempt at a Solution



I'm not exactly sure what the "expected" net winnings mean. I've been searching on the internet, but came up empty.
Thanks for any help you can give me on this.
 
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  • #3
So I'm thinking this is the equation:
(-$100 * 999/1000) + ($75,000 * 1/1000)

That makes the answer: -24.9

I'm not sure if this is correct.
 
  • #4
This gives that a player on average will lose $24.90 on a $100 dollar bet.

Your questions asks for the expected net winnings for the winner so this is not the same thing. I was assuming this question was really about expected values and as you had had difficulty in finding anything about this I gave you the link.

Actually as worded the winner wins $75,000 on a $100 bet so his/her net winnings are $74,900.

Suggest you look again at the wording of the question wherever it came from.
 
  • #5
What? The problem says expected net winnings. If he wins, he wins 75000 so his net winnings are $75000- 100= $74900. If he loses, his net "winnings" are -$100. The probability he will win is 1/1000 (one ticket out of 1000) and the probability he will lose is 999/1000. His expected net winnings are $74900(1/1000)- $100(999/1000)= (74900- 99900)/1000= -25000/1000= -$25.
 
  • #6
HallsofIvy said:
What? The problem says expected net winnings.

The problem as stated by OP is the expected net winnings for the winner .

I was querying whether this was what was actually asked.
 

What is the formula for calculating the expected net winnings from 1,000 raffle tickets?

The formula for calculating the expected net winnings from 1,000 raffle tickets is the probability of winning multiplied by the prize amount, minus the cost of 1,000 raffle tickets. This can be expressed as (P * A) - (C * 1000), where P is the probability of winning, A is the prize amount, and C is the cost of 1,000 raffle tickets.

How do you determine the probability of winning in a raffle?

The probability of winning in a raffle is determined by dividing the number of tickets you hold by the total number of tickets sold. For example, if you hold 10 tickets and there are 100 tickets sold, your probability of winning is 10/100 or 0.1.

What factors can affect the expected net winnings from 1,000 raffle tickets?

The expected net winnings from 1,000 raffle tickets can be affected by several factors such as the total number of tickets sold, the number of prizes available, and the cost of each raffle ticket. Other factors that can impact the expected net winnings include the value of the prize, the probability of winning, and any additional expenses or fees associated with running the raffle.

Is the expected net winnings from 1,000 raffle tickets always accurate?

No, the expected net winnings from 1,000 raffle tickets is an estimated value and may not always accurately reflect the actual winnings. This is because it is based on probability and does not take into account external factors such as unexpected changes in the number of tickets sold or the value of the prize.

How can the expected net winnings from 1,000 raffle tickets be used to make decisions?

The expected net winnings from 1,000 raffle tickets can be used as a guide to make decisions such as whether or not to participate in the raffle or how many tickets to purchase. It can also help determine if the cost of the raffle tickets is worth the potential winnings. However, it should not be the sole factor in making decisions and should be considered along with other factors such as personal preferences and financial situation.

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