1)) There is a raffle with 250 tickets. One ticket will win a prize, one ticket will win
prize, and the rest will win nothing. If you have a ticket, what is the expected payoff

Question

1)) There is a raffle with 250 tickets. One ticket will win a

prize, one ticket will win

prize, and the rest will win nothing. If you have a ticket, what is the expected payoff

UpStudy AI · Accepted Answer

To determine the expected payoff for holding one raffle ticket, we'll analyze the possible outcomes and their associated probabilities.

### Given:
- **Total tickets:** 250
- **Prizes:**
  - **\$160** prize: 1 winning ticket
  - **\$30** prize: 1 winning ticket
  - **No prize:** 248 tickets

### Steps to Calculate Expected Payoff:

1. **Determine the Probability of Each Outcome:**
   - **Winning \$160:** $$ \frac{1}{250} $$
   - **Winning \$30:** $$ \frac{1}{250} $$
   - **Winning Nothing:** $$ \frac{248}{250} $$

2. **Calculate the Expected Value (E):**
   
   The expected value is the sum of each outcome multiplied by its probability.

$$
   E = \left( \frac{1}{250} \times \$160 \right) + \left( \frac{1}{250} \times \$30 \right) + \left( \frac{248}{250} \times \$0 \right)
   $$
   
   Simplifying:
   
   $$
   E = \frac{160 + 30}{250} = \frac{190}{250} = \$0.76
   $$

### **Conclusion:**
The **expected payoff** for holding one raffle ticket is **\$0.76**.

This means that, on average, you'd expect to receive 76 cents per ticket in the long run. However, it's essential to remember that this is a statistical average; in reality, each ticket either wins \$160, \$30, or nothing.
The expected payoff for one raffle ticket is \$0.76.

1)) There is a raffle with 250 tickets. One ticket will win a prize, one ticket will win
prize, and the rest will win nothing. If you have a ticket, what is the expected payoff

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