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Sagot :
To solve the given question, we need to calculate the relative frequencies of landing on the number 4 and on a prime number based on Jamie's recorded outcomes. Let's go through this step-by-step.
### Step-by-Step Solution
#### Step 1: Determine the Total Number of Rolls
First, we need to find out the total number of times Jamie rolled the dice by summing up all the frequencies:
[tex]\[ \text{Total Number of Rolls} = 15 + 2 + 5 + 16 = 38 \][/tex]
### Part (a): Relative Frequency of Landing on the Number 4
#### Step 2: Identify the Frequency of the Outcome 4
From the table, we see that the number 4 appeared 16 times.
#### Step 3: Calculate the Relative Frequency
The relative frequency is calculated by dividing the frequency of the outcome by the total number of rolls:
[tex]\[ \text{Relative Frequency of Landing on 4} = \frac{\text{Frequency of 4}}{\text{Total Rolls}} = \frac{16}{38} \approx 0.4211 \][/tex]
Thus, the relative frequency of landing on the number 4 is approximately [tex]\(0.4211\)[/tex].
### Part (b): Relative Frequency of Landing on a Prime Number
#### Step 4: Identify Prime Numbers
We need to identify which of the outcomes are prime numbers. The prime numbers less than or equal to 6 are 2 and 3.
#### Step 5: Identify the Frequencies of Prime Numbers
From the table:
- The frequency of the outcome 2 is 2.
- The frequency of the outcome 3 is 5.
#### Step 6: Calculate the Total Frequency of Prime Numbers
[tex]\[ \text{Total Frequency of Prime Numbers} = 2 + 5 = 7 \][/tex]
#### Step 7: Calculate the Relative Frequency
The relative frequency of landing on a prime number is calculated by dividing the total frequency of prime numbers by the total number of rolls:
[tex]\[ \text{Relative Frequency of Landing on a Prime Number} = \frac{\text{Total Frequency of Prime Numbers}}{\text{Total Rolls}} = \frac{7}{38} \approx 0.1842 \][/tex]
Thus, the relative frequency of landing on a prime number is approximately [tex]\(0.1842\)[/tex].
### Summary of Results
- The relative frequency of landing on the number 4 is approximately [tex]\(0.4211\)[/tex].
- The relative frequency of landing on a prime number is approximately [tex]\(0.1842\)[/tex].
### Step-by-Step Solution
#### Step 1: Determine the Total Number of Rolls
First, we need to find out the total number of times Jamie rolled the dice by summing up all the frequencies:
[tex]\[ \text{Total Number of Rolls} = 15 + 2 + 5 + 16 = 38 \][/tex]
### Part (a): Relative Frequency of Landing on the Number 4
#### Step 2: Identify the Frequency of the Outcome 4
From the table, we see that the number 4 appeared 16 times.
#### Step 3: Calculate the Relative Frequency
The relative frequency is calculated by dividing the frequency of the outcome by the total number of rolls:
[tex]\[ \text{Relative Frequency of Landing on 4} = \frac{\text{Frequency of 4}}{\text{Total Rolls}} = \frac{16}{38} \approx 0.4211 \][/tex]
Thus, the relative frequency of landing on the number 4 is approximately [tex]\(0.4211\)[/tex].
### Part (b): Relative Frequency of Landing on a Prime Number
#### Step 4: Identify Prime Numbers
We need to identify which of the outcomes are prime numbers. The prime numbers less than or equal to 6 are 2 and 3.
#### Step 5: Identify the Frequencies of Prime Numbers
From the table:
- The frequency of the outcome 2 is 2.
- The frequency of the outcome 3 is 5.
#### Step 6: Calculate the Total Frequency of Prime Numbers
[tex]\[ \text{Total Frequency of Prime Numbers} = 2 + 5 = 7 \][/tex]
#### Step 7: Calculate the Relative Frequency
The relative frequency of landing on a prime number is calculated by dividing the total frequency of prime numbers by the total number of rolls:
[tex]\[ \text{Relative Frequency of Landing on a Prime Number} = \frac{\text{Total Frequency of Prime Numbers}}{\text{Total Rolls}} = \frac{7}{38} \approx 0.1842 \][/tex]
Thus, the relative frequency of landing on a prime number is approximately [tex]\(0.1842\)[/tex].
### Summary of Results
- The relative frequency of landing on the number 4 is approximately [tex]\(0.4211\)[/tex].
- The relative frequency of landing on a prime number is approximately [tex]\(0.1842\)[/tex].
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