Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Jamie rolled a six-sided die a number of times and recorded the outcomes in the table below.

Work out the relative frequency of landing on:

a) the number 4.
b) a prime number.

Give your answers as decimals.

\begin{tabular}{|c|c|}
\hline Outcome & Frequency \\
\hline 1 & 15 \\
\hline 2 & 2 \\
\hline 3 & 5 \\
\hline 4 & 16 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
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].
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.