Question

In a raffle, one ticket will win a $360 prize, and the other tickets will win nothing. There are 250 in the raffle. X is the payoff for one ticket in the raffle. Write the probability distribution of X in the table to the right. Which two probabilities are correct for the blanks.
(2 Points)

Please select 2 options.

0.04

0.96

0.004

0.996

Answer 1

To find the probability distribution of the random variable \( X \), which represents the payoff for one ticket in the raffle, we need to consider the two possible outcomes for your ticket:

1. Winning the prize of $360 (this happens with probability \( P(X = 360) \)).
2. Not winning anything (this happens with probability \( P(X = 0) \)).

Given there are 250 tickets, and only 1 ticket wins the prize, the probabilities are calculated as follows:

- The probability of winning the prize:
\[
P(X = 360) = \frac{1}{250} = 0.004
\]

- The probability of not winning anything:
\[
P(X = 0) = \frac{249}{250} = 0.996
\]

Thus, the probability distribution of \( X \) can be summarized as:

| \( X \) | Probability |
|-----------|---------------|
| 360 | 0.004 |
| 0 | 0.996 |

The two correct probabilities for the blanks you were looking for are:

- **0.004** (probability of winning $360)
- **0.996** (probability of winning $0)