Questions: A sample of consumers was surveyed about their purchasing habits, and the responses are summarized in the table below. Compute each probability (as a decimal rounded to two places). Shops online for pet food and supplies Shops at a physical store for pet food and supplies Total ------------ Lives within 10 miles of the nearest pet supply store 39 410 449 Lives more than 10 miles away from the nearest pet supply store 161 90 251 Total 200 500 700 What is the probability a consumer lives more than 10 miles away from the nearest pet supply store and shops online for pet food and supplies? Ex: 0.12

A sample of consumers was surveyed about their purchasing habits, and the responses are summarized in the table below. Compute each probability (as a decimal rounded to two places).

Shops online for pet food and supplies Shops at a physical store for pet food and supplies Total
------------
Lives within 10 miles of the nearest pet supply store 39 410 449
Lives more than 10 miles away from the nearest pet supply store 161 90 251
Total 200 500 700

What is the probability a consumer lives more than 10 miles away from the nearest pet supply store and shops online for pet food and supplies?

Ex: 0.12

Transcript text: Question 16 of 24 1 2 A sample of consumers was surveyed about their purchasing habits, and the responses are summarized in the table below. Compute each probability (as a decimal rounded to two places). 3 4 5 \begin{tabular}{|c|l|l|l|} \hline & \begin{tabular}{c} Shops online for pet \\ food and supplies \end{tabular} & \begin{tabular}{l} Shops at a physical store \\ for pet food and supplies \end{tabular} & Total \\ \hline \begin{tabular}{c} Lives within 10 miles of \\ the nearest pet supply store \end{tabular} & 39 & 410 & 449 \\ \hline \begin{tabular}{c} Lives more than 10 miles away \\ from the nearest pet supply store \end{tabular} & 161 & 90 & 251 \\ \hline Total & 200 & 500 & 700 \\ \hline \end{tabular} 7 8 What is the probability a consumer lives more than 10 miles away from the nearest pet supply store and shops online for pet food and supplies? 9 Ex: 0.12 10 11

Solution

Solution Steps

To find the probability that a consumer lives more than 10 miles away from the nearest pet supply store and shops online for pet food and supplies, we need to divide the number of consumers who meet both criteria by the total number of consumers surveyed. This will give us the probability as a decimal.

Step 1: Identify the Relevant Values

From the data provided, we have:

Number of consumers who live more than 10 miles away and shop online: \( 161 \)
Total number of consumers surveyed: \( 700 \)

Step 2: Calculate the Probability

The probability \( P \) that a consumer lives more than 10 miles away from the nearest pet supply store and shops online for pet food and supplies can be calculated using the formula:

\[ P = \frac{\text{Number of consumers who live more than 10 miles and shop online}}{\text{Total number of consumers}} \]

Substituting the values:

\[ P = \frac{161}{700} \]

Step 3: Simplify and Round the Probability

Calculating the above expression gives:

\[ P \approx 0.230 \]

Rounding this to two decimal places results in:

\[ P \approx 0.23 \]