To analyze the probability distribution for this raffle, let's take a step-by-step approach to determine the probability of each possible outcome: winning no award, an award of [tex]$30, $[/tex]50, or [tex]$100.
1. Determine the total number of tickets:
- Addison sells a total of 100 tickets.
2. List the number of each type of award:
- 1 prize of $[/tex]100
- 4 prizes of [tex]$50
- 10 prizes of $[/tex]30
3. Calculate the probability of winning each type of prize:
- Probability of winning [tex]$100:
- There is 1 prize out of 100 tickets.
\[
\text{Probability} = \frac{1}{100} = 0.01
\]
- Probability of winning $[/tex]50:
- There are 4 prizes out of 100 tickets.
[tex]\[
\text{Probability} = \frac{4}{100} = 0.04
\][/tex]
- Probability of winning [tex]$30:
- There are 10 prizes out of 100 tickets.
\[
\text{Probability} = \frac{10}{100} = 0.10
\]
4. Calculate the probability of not winning any award:
- Total prizes being awarded are 1 (for $[/tex]100) + 4 (for [tex]$50) + 10 (for $[/tex]30) = 15 prizes.
- The rest of the tickets (100 - 15 = 85) do not win any prize.
[tex]\[
\text{Probability of not winning} = \frac{85}{100} = 0.85
\][/tex]
5. Summarize the probability distribution in a table:
[tex]\[
\begin{array}{|c|c|}
\hline \multicolumn{2}{|c|}{\text{Distribution of Awards}} \\
\hline \text{Prize} & P(x) \\
\hline \text{None} & 0.85 \\
\hline \$30 & 0.10 \\
\hline \$50 & 0.04 \\
\hline \$100 & 0.01 \\
\hline
\end{array}
\][/tex]
This table correctly displays the probability distribution for the raffle. Each probability value reflects the chance of a ticket being associated with winning a specific prize or not winning at all.
