Determine expected value of each winnings

In summary, the charitable organization is considering two scenarios for a raffle to raise money, one with 3,000 tickets sold at $1 each and the other with 2,000 tickets sold at $2 each. The expected value for the winnings of the players in Case A is $0.17 per ticket, while the expected value for the winnings of the players in Case B is $0.25 per ticket. The total payout for both cases would be $500.
  • #1
Kristinanne
10
0
1. Homework Statement [/b]

A charitable organization is raffling a trip worth $500 to raise money and needs to decide which of the following scenarios would be the most profitable based on expected value of the proposed game.

Case A: 3,000 tickets are sold at $1.00 each.

Case B, 2,000 tickets are sold at $2.00 each.

1. Determine the expected value for the winnings of the players in Case A.
2. Determine the expected value for the winnings of the players in Case B.



Homework Equations





The Attempt at a Solution



To do this, wouldn't I have to know what the payout is?
 
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  • #2


You don't think the payout is the $500 trip?
 
  • #3


I was thinking that. That would make a and b $500.00 then correct?
 
  • #4


That would be the total payout for the raffle.

For each dollar though what is the expected return to each ticket holder taking into account their chance of winning?
 
  • #5


For instance if I buy a ticket for $1 in a lottery with a 1:1,000,000 chance of winning - 1M tickets sold - then my expected winning is $1 return.

I only have one chance of winning ... but if I do I get $1,000,000 right?
 

1. What is the expected value of each winnings?

The expected value of each winnings is the sum of all possible outcomes, weighted by their respective probabilities. It provides an estimate of the average amount that a player can expect to win over many repetitions of the game.

2. How is the expected value calculated?

The expected value is calculated by multiplying the value of each outcome by its probability and then summing all of these values together. The formula is: expected value = (outcome 1 x probability 1) + (outcome 2 x probability 2) + ... + (outcome n x probability n).

3. What does a positive expected value mean?

A positive expected value means that, on average, the player can expect to win money over a large number of repetitions of the game. This indicates a favorable outcome for the player.

4. Is the expected value a guarantee of winning?

No, the expected value is not a guarantee of winning. It is simply a theoretical value that represents the average outcome over many repetitions of the game. In any individual game, the actual outcome may be different from the expected value.

5. How can the expected value be used in decision-making?

The expected value can be used in decision-making by comparing it to the cost of playing the game. If the expected value is positive, it may be a good decision to play the game as the player can expect to make a profit in the long run. However, if the expected value is negative, it may be better to avoid playing the game as the player can expect to lose money over time.

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