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To solve for \( P(B \mid A) \), we need to use the formula for conditional probability:

\[
P(B \mid A) = \frac{P(A \text{ and } B)}{P(A)}
\]

From the information provided in the problem:
- \( P(A) = 0.20 \)
- \( P(B) = 0.25 \)
- \( P(A \text{ and } B) = 0.10 \)

Substituting these values into the formula:

\[
P(B \mid A) = \frac{0.10}{0.20} = 0.50
\]

So the correct answer is \( C. 0.50 \).

Would you like further details or have any questions?

Here are some related questions you might find useful:
1. How is conditional probability used in real-world applications?
2. What is the difference between independent and dependent events?
3. How would you find \( P(A \mid B) \) given the same data?
4. What are some common misconceptions about conditional probability?
5. How can the multiplication rule be used to find \( P(A \text{ and } B) \)?
6. What is Bayes' Theorem and how does it relate to conditional probability?
7. How can conditional probability be visualized using a probability tree diagram?
8. What are some examples of conditional probability problems in statistics?

**Tip:** Always check if events are independent before applying conditional probability formulas, as it can simplify the calculations!

Learn how to calculate conditional probability P(B | A) with a step-by-step solution. Includes the conditional probability formula and application to given probabilities: P(A) = 0.20, P(B) = 0.25, P(A and B) = 0.10. Suitable for advanced high school students.

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