Question

For a fundraiser, there is a raffle with 125 tickets. One ticket will win a $700 prize, and the remaining tickets will win nothing. 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.

Answer 1

To create the probability distribution of \(X\), the payoff for one ticket in the raffle, we first need to define the possible outcomes and their corresponding probabilities.

In this case, there are two possible outcomes for a single ticket:

1. Winning the $700 prize (which occurs when you hold the winning ticket).
2. Not winning anything (which occurs when you hold one of the other 124 tickets).

Next, we calculate the probabilities:

1. Probability of winning ($700):
\[
P(X = 700) = \frac{1}{125}
\]

2. Probability of not winning ($0):
\[
P(X = 0) = \frac{124}{125}
\]

Now, we can present these probabilities in a probability distribution table:

\[
\begin{array}{|c|c|}
\hline
\text{Payoff } (X) & \text{Probability } P(X) \\
\hline
700 & \frac{1}{125} \\
0 & \frac{124}{125} \\
\hline
\end{array}
\]

Thus, the probabilities for the blanks are:
- \(\frac{1}{125}\) for winning ($700)
- \(\frac{124}{125}\) for not winning ($0)