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.