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The problem asks to find the probability that a randomly selected person prefers dogs, given that they are female.

This is a conditional probability question, where we are asked to find:

\[
P(\text{Prefers Dogs} \mid \text{Female}) = \frac{P(\text{Female and Prefers Dogs})}{P(\text{Female})}
\]

From the table:
- The number of females who prefer dogs = 9
- The total number of females = 12 (Prefer cats) + 9 (Prefer dogs) = 21

Thus, the probability is:

\[
P(\text{Prefers Dogs} \mid \text{Female}) = \frac{9}{21}
\]

Now, simplify the fraction:

\[
\frac{9}{21} = \frac{3}{7}
\]

So, the probability is \( \frac{3}{7} \).

Would you like further details or have any questions?

Here are 5 related questions to expand on this:
1. What is the probability that a randomly selected female prefers cats?
2. What is the probability that a randomly selected person is male and prefers dogs?
3. What is the probability that a randomly selected person prefers dogs, regardless of gender?
4. How would you calculate the probability that a randomly selected person prefers cats, given they are male?
5. What is the total probability of selecting someone who prefers either cats or dogs?

**Tip:** When dealing with conditional probability, always pay attention to the condition and restrict the total sample space accordingly.

For the table below, find the probability of a randomly selected person prefers dogs, given that they are female. Show the answer as a fraction in reduced terms.

Learn how to calculate the probability that a randomly selected female prefers dogs using conditional probability concepts. This problem explores probability calculations using tables, fractions, and simplification techniques. Suitable for students in Grades 7-9.

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