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.
