https://file.aiquickdraw.com/mathbot/file/1728227733898an1sawcr.jpg

The question asks for the value of \( k \) given the probability that a person picked has a pet given that the person is a female.

### Let's break it down:
- From the table:
  - Number of females who have pets: \( 24 \)
  - Number of females in total: \( 24 + 21 = 45 \)

### Formula for conditional probability:
The probability that a person has a pet given that the person is female is:

\[
P(\text{Has pet} | \text{Female}) = \frac{\text{Number of females with pets}}{\text{Total number of females}} = \frac{24}{45}
\]

We are given that:

\[
P(\text{Has pet} | \text{Female}) = \frac{k}{15}
\]

Thus, equate the two probabilities:

\[
\frac{24}{45} = \frac{k}{15}
\]

Now, solve for \( k \):

\[
k = \frac{24 \times 15}{45} = \frac{360}{45} = 8
\]

Therefore, the value of \( k \) is \( 8 \).

---

Do you have any questions or need further details?

Here are 5 related questions you might find interesting:
1. What is the probability that a randomly selected person has a pet?
2. What is the probability that a person picked is female and has a pet?
3. What is the probability that a person does not have a pet given that the person is male?
4. How would the result change if the numbers of pet owners were different?
5. Can you find the probability that the person picked is male, given they do not have a pet?

**Tip:** When solving probability questions, always identify the total possible outcomes and specific favorable outcomes.

The probability a person picked has a pet given that this person is a female is \( \frac{k}{15} \). What is the value of k?

This problem involves finding the value of k in a conditional probability setup. Using survey data about pet ownership among males and females, the solution demonstrates how to calculate the probability of having a pet given that the person is female. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation