Pregunta
For a fundraiser, there is a raffle with 1,000 tickets. One ticket will win a
prize,
even tickets will win a
prize, nine tickets will win a
prize, and the rest will win
othing. If you have a ticket, what is the expected payoff?
even tickets will win a
othing. If you have a ticket, what is the expected payoff?
Ask by Willis Stephens. in the United States
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The expected payoff for a ticket is $116.10.
Solución
To find the expected payoff for a ticket in the raffle, we need to calculate the expected value based on the probabilities of winning each prize and the corresponding amounts.
Known Conditions:
- Total tickets:
- Prizes:
- 1 ticket wins
- 500 tickets (even tickets) win
- 9 tickets win
- The rest win nothing.
- 1 ticket wins
Step-by-Step Calculation:
-
Calculate the probabilities of winning each prize:
- Probability of winning
: - Probability of winning
: - Probability of winning
: - Probability of winning nothing:
- Probability of winning
-
Calculate the expected value (EV):
The expected value is calculated as follows:Substituting the probabilities and prizes: -
Perform the calculations:
- For
: - For
: - For
: - For nothing:
- For
-
Sum the expected values:
Final Answer:
The expected payoff for a ticket in the raffle is
.
Respondido por UpStudy AI y revisado por un tutor profesional
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Extra Insights
To determine the expected payoff for a single ticket, we first identify the prizes and their probabilities. There is 1 grand prize of
, 500 even tickets (2, 4, 6, etc.) each winning
, and 9 tickets winning
. Out of 1,000 tickets, that means 490 tickets win nothing.
Now, we calculate the expected payoff:
- Grand Prize:
ticket wins with a probability of . - Even Prize:
tickets win with a probability of . - Minor Prizes:
tickets win with a probability of . - No Prize:
tickets win with a probability of .
Now, we calculate the contribution from each possible outcome:
- Grand Prize:
- Even Prize:
- Minor Prizes:
- No Prize:
Adding these together gives the expected payoff:
Thus, the expected payoff for one ticket is:
Expected Payoff = $116.1

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