Let's analyze the probability distribution for Addison's raffle.
Addison sold 100 tickets, and these are the prizes:
- 1 award of [tex]$100
- 4 awards of $[/tex]50
- 10 awards of [tex]$30
- The remaining tickets do not win any prize.
First, calculate the number of tickets that do not win any prize:
\[ \text{Total tickets} - (\text{number of $[/tex]100 awards} + \text{number of [tex]$50 awards} + \text{number of $[/tex]30 awards}) \]
[tex]\[ 100 - (1 + 4 + 10) \][/tex]
[tex]\[ 100 - 15 = 85 \][/tex]
This means 85 tickets result in no prize. Next, we calculate the probabilities for each outcome by dividing the number of corresponding tickets by the total number of tickets (100).
For no prize (none):
[tex]\[ P(\text{none}) = \frac{85}{100} = 0.85 \][/tex]
For the [tex]$30 prize:
\[ P(\$[/tex]30) = \frac{10}{100} = 0.1 \]
For the [tex]$50 prize:
\[ P(\$[/tex]50) = \frac{4}{100} = 0.04 \]
For the [tex]$100 prize:
\[ P(\$[/tex]100) = \frac{1}{100} = 0.01 \]
Hence, the probability distribution is as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
\multicolumn{2}{|c|}{\text{Distribution of Awards}} \\
\hline
\text{Prize} & P(x) \\
\hline
\text{none} & 0.85 \\
\hline
\$30 & 0.1 \\
\hline
\$50 & 0.04 \\
\hline
\$100 & 0.01 \\
\hline
\end{array}
\][/tex]
Therefore, the correct table displaying the probability distribution should be:
[tex]\[
\begin{array}{|c|c|}
\hline
\multicolumn{2}{|c|}{\text{Distribution of Awards}} \\
\hline
\text{Prize} & P(x) \\
\hline
\text{none} & 0.85 \\
\hline
\$30 & 0.1 \\
\hline
\$50 & 0.04 \\
\hline
\$100 & 0.01 \\
\hline
\end{array}
\][/tex]
