Question

In a raffle, one ticket out of 100 will win a $190 prize, two tickets will win a $90 prize, and four tickets will win a $50 prize. The other tickets will win nothing. X is the payoff for one ticket in the raffle. Rank the probabilities to match the money amounts.
(4 Points)

Answer 1

To find the probabilities of each possible outcome for the payoff \(X\) in the raffle, we need to analyze the tickets and their corresponding payoffs.

1. **Winning $190:**
- There is 1 ticket that wins $190 out of 100 tickets.
- Probability = \( \frac{1}{100} \)

2. **Winning $90:**
- There are 2 tickets that win $90 out of 100 tickets.
- Probability = \( \frac{2}{100} = \frac{1}{50} \)

3. **Winning $50:**
- There are 4 tickets that win $50 out of 100 tickets.
- Probability = \( \frac{4}{100} = \frac{1}{25} \)

4. **Winning nothing:**
- The remaining tickets (100 - 1 - 2 - 4 = 93) win nothing out of 100 tickets.
- Probability = \( \frac{93}{100} \)

Now, we can summarize the payoffs and their probabilities:

- Payoff $190: Probability \( \frac{1}{100} \)
- Payoff $90: Probability \( \frac{2}{100} \) or \( \frac{1}{50} \)
- Payoff $50: Probability \( \frac{4}{100} \) or \( \frac{1}{25} \)
- Payoff $0: Probability \( \frac{93}{100} \)

Finally, let’s rank the probabilities associated with the money amounts:

1. **$190:** Probability = \( \frac{1}{100} \)
2. **$90:** Probability = \( \frac{2}{100} \)
3. **$50:** Probability = \( \frac{4}{100} \)
4. **$0:** Probability = \( \frac{93}{100} \)

Thus, in ranked order from highest probability to lowest:

- $0 (93/100)
- $50 (4/100)
- $90 (2/100)
- $190 (1/100)