There is a raffle with 250 tickets. One ticket will wh 200 prize, five tickets will win a 90 prize, seventeen tickets will win a 40 prize, and the other tickets will win nothing. X is the payoff for one ticket in the raffle. Write the probability distribution of X in the table below Write each probability as an exact decimal. x & P(x) 4) & 4) & 4) & 4) &

## Step 1: Identify the possible payoffs
### The possible payoffs for one ticket in the raffle are $\$200$, $\$90$, $\$40$, and $\$0$.

## Step 2: Determine the number of tickets for each payoff
### There is 1 ticket that wins $\$200$, 5 tickets that win $\$90$, 17 tickets that win $\$40$, and the remaining tickets (250 - 1 - 5 - 17 = 227) win nothing ($0).

## Step 3: Calculate the probabilities for each payoff
### The probability $P(X = x)$ is calculated by dividing the number of tickets with payoff $x$ by the total number of tickets (250).
- For $X = 200$: $P(X = 200) = \frac{1}{250} = 0.004$
- For $X = 90$: $P(X = 90) = \frac{5}{250} = 0.02$
- For $X = 40$: $P(X = 40) = \frac{17}{250} = 0.068$
- For $X = 0$: $P(X = 0) = \frac{227}{250} = 0.908$

## Step 4: Fill in the table with the calculated probabilities
### Using the calculated probabilities, we can fill in the table as follows:

$$\begin{array}{|c|c|} \hline X & P(X) \\ \hline 200 & 0.004 \\ \hline 90 & 0.02 \\ \hline 40 & 0.068 \\ \hline 0 & 0.908 \\ \hline \end{array}$$