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 , .## Step 2: Determine the number of tickets for each payoff### There is 1 ticket that wins , 17 tickets that win 0).## Step 3: Calculate the probabilities for each payoff### The probability \( P(X = x) \) is calculated by dividing the number of tickets with payoff by the total number of tickets (250).- For : \( P(X = 200) = \frac{1}{250} = 0.004 \)- For : \( P(X = 90) = \frac{5}{250} = 0.02 \)- For : \( P(X = 40) = \frac{17}{250} = 0.068 \)- For : \( P(X = 0) = \frac{227}{250} = 0.908 \)## Step 4: Fill in the table with the calculated probabilities### Using the calculated probabilities, we can fill in the table as follows: