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Let's analyze and solve the given questions in parts (b) and (c).

### Part (b) - Find the exact value of \( q \) and \( r \)

From the Venn diagram and given information:
- \( P(B' \cap D') = \frac{7}{10} \)
- \( P(C|D) = \frac{3}{5} \)

**Step 1: Find \( r \) using conditional probability:**
The formula for conditional probability is:
\[
P(C|D) = \frac{P(C \cap D)}{P(D)}
\]
Let \( r \) represent the probability \( P(C \cap D) \) and let \( s \) represent \( P(D) \). We are given that \( P(C|D) = \frac{3}{5} \), so:
\[
\frac{r}{s} = \frac{3}{5}
\]
Thus, \( r = \frac{3}{5}s \).

**Step 2: Use \( P(B' \cap D') \):**
We know that:
\[
P(B' \cap D') = 1 - P(B \cup D)
\]
Given that \( P(B' \cap D') = \frac{7}{10} \), we can write:
\[
1 - P(B \cup D) = \frac{7}{10}
\]
Thus,
\[
P(B \cup D) = 1 - \frac{7}{10} = \frac{3}{10}
\]
We also know that:
\[
P(B \cup D) = P(B) + P(D) - P(B \cap D)
\]
Given that \( P(B) = 0.12 \) (from the diagram) and assuming \( P(B \cap D) = 0 \) (since the Venn diagram does not indicate any overlap between \( B \) and \( D \)), we have:
\[
P(B \cup D) = 0.12 + s
\]
Setting this equal to \( \frac{3}{10} \):
\[
0.12 + s = \frac{3}{10}
\]
\[
s = \frac{3}{10} - 0.12 = 0.18
\]

So, \( s = 0.18 \).

**Step 3: Find \( r \):**
Now, substitute \( s = 0.18 \) into the equation \( r = \frac{3}{5}s \):
\[
r = \frac{3}{5} \times 0.18 = 0.108
\]

### Part (b) Solution:
- \( r = 0.108 \)
- \( s = 0.18 \)

### Part (c) - Find the exact value of \( s \)
This has already been calculated above as part of solving part (b). Thus, the value of \( s \) is:

\[
s = 0.18
\]

---

Would you like further clarifications or detailed explanations on any part of this solution? Here are some additional questions to consider:

1. How is conditional probability applied in part (b)?
2. Can we find \( P(A \cap C) \) with the given information?
3. What does \( P(B' \cap D') \) represent in this problem context?
4. How would the problem change if \( P(B \cap D) \neq 0 \)?
5. Can we solve for the value of \( p \) or any other missing probabilities?

**Tip:** When dealing with Venn diagrams and probabilities, remember to use basic set operations such as union and intersection, and don't forget about complementary events!

Explore how to solve probability questions using conditional probability and Venn diagrams. Learn how to find the exact values of probabilities using given conditions, including P(C|D) = 3/5 and P(B' ∩ D') = 7/10. Perfect for Grades 11-12 students.

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