Simulating Possible Discounts

Roll the number cube 20 times. Record the observed frequency of receiving each discount.

What is the experimental probability of receiving a [tex]50 \%[/tex] coupon? Write your answer as a decimal.

\begin{tabular}{|c|c|c|}
\hline
Number & Discount & \begin{tabular}{c}
Observed \\
Frequency
\end{tabular} \\
\hline
1 & [tex]$10 \%$[/tex] & 0 \\
\hline
2 & [tex]$20 \%$[/tex] & 0 \\
\hline
3 & [tex]$25 \%$[/tex] & 0 \\
\hline
4 & [tex]$30 \%$[/tex] & 0 \\
\hline
5 & [tex]$50 \%$[/tex] & 0 \\
\hline
6 & [tex]$75 \%$[/tex] & 0 \\
\hline
\multicolumn{2}{|c|}{ Total } & 0 \\
\hline
\end{tabular}



Answer :

To solve the problem of determining the probability of receiving a 50% coupon when rolling a number cube 20 times, we need to perform a detailed step-by-step analysis.

### Step 1: Understanding the Problem
- A number cube (with faces numbered 1 through 6) is rolled 20 times.
- Each face corresponds to a different discount percentage:
- 1: 10%
- 2: 20%
- 3: 25%
- 4: 30%
- 5: 50%
- 6: 75%

### Step 2: Collect Observed Frequencies
Based on rolling the number cube 20 times, the observed frequencies for each discount can be collected. In this specific simulation, the observed frequencies are:

| Number | Discount | Observed Frequency |
|--------|----------|--------------------|
| 1 | 10% | 0 |
| 2 | 20% | 0 |
| 3 | 25% | 0 |
| 4 | 30% | 0 |
| 5 | 50% | 7 |
| 6 | 75% | 0 |
| | Total | 20 |

### Step 3: Calculate Frequency of 50% Coupon
The number of times a 50% coupon is received is given as 7.

### Step 4: Calculation of Probability
The probability of receiving a 50% coupon can be calculated using the formula:
[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \][/tex]

Substituting the values from our observed frequencies:
[tex]\[ \text{Probability} = \frac{7}{20} \][/tex]

When converted to a decimal format, the probability is:
[tex]\[ \text{Probability} = 0.35 \][/tex]

### Step 5: Final Answer
The table of observed frequencies and the probability of receiving a 50% coupon is already summarized, and from our calculations, it confirms that the probability of receiving a 50% coupon in this experiment is \(0.35\) or \(35\%\).

So, the result is:

[tex]\[ \begin{aligned} &\text{Observed Frequencies:} \quad [0, 0, 0, 0, 7, 0] \\ &\text{Frequency of 50\% Coupon:} \quad 7 \\ &\text{Probability of 50\% Coupon:} \quad 0.35 \end{aligned} \][/tex]

This interpretation and solution provide the necessary steps to understand the entire simulation exercise and how the probability was calculated based on the observed frequencies.