To find the conditional probability $P(B \mid A)$, we use the formula:

$P(B \mid A) = \frac{P(A \cap B)}{P(A)}$

From the Euler diagram in the image:

• $P(A \cap B) = 0.08$ (the intersection of events A and B)
• $P(A) = 0.08 + 0.41 = 0.49$ (the total probability of event A)

Now, calculating:

$P(B \mid A) = \frac{0.08}{0.49} \approx 0.1633$

Final Answer:

$P(B \mid A) \approx 0.16 \text{ (rounded to two decimal places)}$

Would you like a more detailed explanation? Here are some related questions:

1. What does conditional probability represent in real-world scenarios?
2. How can we generalize this formula for three or more events?
3. What is the relationship between conditional probability and independence?
4. How would the probability change if event $A$ had a different probability?
5. How can Venn diagrams help visualize probability problems?

Tip: Conditional probability is useful in Bayesian inference, where we update probabilities based on new evidence.