https://file.aiquickdraw.com/mathbot/file/172683904358045uffbz4.jpg

Let's analyze the Venn diagram and the related probabilities.

The question consists of the following parts:
- The events \( A \), \( B \), \( C \), and \( D \) are shown in a Venn diagram with probabilities labeled as \( p \), \( q \), \( r \), and \( s \).
- The diagram contains two main groups: one with sets \( A \) and \( B \), and the other with sets \( C \) and \( D \).

From the image:
- The probability of \( A \), which is entirely within one circle, is \( 0.13 \).
- The probability of \( B \), which is also within another circle, is \( 0.12 \).
- The values \( p \), \( q \), \( r \), and \( s \) are not directly given, but they represent other parts of the diagram.

The tasks:
1. **(i) Write down the value of \( P(A) \):**
   - From the diagram, \( P(A) = 0.13 \).
  
2. **(ii) Write down the value of \( P(A \cap B) \):**
   - Since there is no overlapping area between \( A \) and \( B \) (as they are in separate circles with no intersection shown), \( P(A \cap B) = 0 \).

3. **(iii) Write down the value of \( P(A \cap C) \):**
   - \( A \) and \( C \) are also in different parts of the diagram, with no visible intersection. Hence, \( P(A \cap C) = 0 \).

Would you like to go through any part of the solution in more detail, or do you have any questions?

Here are five related questions that can extend the topic:
1. What is the probability of \( P(A \cup B) \)?
2. How do you calculate \( P(C \cap D) \) from the Venn diagram?
3. Can you find \( P(C \cup D) \) from the values \( p \), \( q \), \( r \), and \( s \)?
4. What is the general formula for finding the probability of \( A \cup B \cup C \cup D \)?
5. How would overlapping regions affect the calculation of probabilities in a Venn diagram?

**Tip:** When working with Venn diagrams, always look for intersections and unions carefully, as they significantly impact how probabilities are combined.

The Venn diagram shows the events A, B, C, and D, where p, q, r, and s are probabilities. (a) Write down the value of (i) P(A) (ii) P(A∩B) (iii) P(A∩C)

Learn how to calculate probabilities using Venn diagrams with the events A, B, C, and D. Understand the values of P(A), P(A∩B), and P(A∩C) by interpreting the diagram and applying probability rules. Suitable for students in Grades 9-12.

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