Question

1. what is the probability that a randomly selected customer who would like to see the toy department expanded is younger than 10?

Explanation:

To solve this probability problem, we typically need a table or data showing the number of customers who want the toy department expanded and their ages (specifically those younger than 10 and the total in that group). Since that data isn't provided here, we can outline the general steps:

Step 1: Identify the relevant counts

Let’s assume we have a table with two categories: "Age < 10" and "Total who want toy department expanded". Let \( n(\text{Age} < 10 \cap \text{Want toy expanded}) \) be the number of customers younger than 10 who want the toy department expanded, and \( n(\text{Want toy expanded}) \) be the total number of customers who want the toy department expanded.

Step 2: Apply the conditional probability formula

The probability \( P(\text{Age} < 10 | \text{Want toy expanded}) \) is given by the formula:

$$ P(\text{Age} < 10 | \text{Want toy expanded}) = \frac{n(\text{Age} < 10 \cap \text{Want toy expanded})}{n(\text{Want toy expanded})} $$

For example, if there are 20 customers younger than 10 who want the toy department expanded and 50 total customers who want the toy department expanded, then:

$$ P = \frac{20}{50} = \frac{2}{5} = 0.4 $$

Since the specific data (like the table) is missing from the problem, we can't calculate the exact value, but the above steps show how to solve it once the data is provided.

If we assume a common example (e.g., from a typical survey table where, say, 30 out of 100 customers who want toy expansion are younger than 10), the probability would be \( \frac{30}{100} = 0.3 \) or \( \frac{3}{10} \).

To get the exact answer, we need the frequency table or data listing the number of customers in each category (age < 10 and total who want toy department expanded).

Answer:

To solve this probability problem, we typically need a table or data showing the number of customers who want the toy department expanded and their ages (specifically those younger than 10 and the total in that group). Since that data isn't provided here, we can outline the general steps:

Step 1: Identify the relevant counts

Let’s assume we have a table with two categories: "Age < 10" and "Total who want toy department expanded". Let \( n(\text{Age} < 10 \cap \text{Want toy expanded}) \) be the number of customers younger than 10 who want the toy department expanded, and \( n(\text{Want toy expanded}) \) be the total number of customers who want the toy department expanded.

Step 2: Apply the conditional probability formula

The probability \( P(\text{Age} < 10 | \text{Want toy expanded}) \) is given by the formula:

$$ P(\text{Age} < 10 | \text{Want toy expanded}) = \frac{n(\text{Age} < 10 \cap \text{Want toy expanded})}{n(\text{Want toy expanded})} $$

For example, if there are 20 customers younger than 10 who want the toy department expanded and 50 total customers who want the toy department expanded, then:

$$ P = \frac{20}{50} = \frac{2}{5} = 0.4 $$

Since the specific data (like the table) is missing from the problem, we can't calculate the exact value, but the above steps show how to solve it once the data is provided.

If we assume a common example (e.g., from a typical survey table where, say, 30 out of 100 customers who want toy expansion are younger than 10), the probability would be \( \frac{30}{100} = 0.3 \) or \( \frac{3}{10} \).

To get the exact answer, we need the frequency table or data listing the number of customers in each category (age < 10 and total who want toy department expanded).