To solve for $P(A \cup B)$ in different scenarios, we need to use the basic rules of probability.

Part (ក): When $A$ and $B$ are not mutually exclusive (dependent events)

When two events $A$ and $B$ are not mutually exclusive, their union probability is given by: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

However, in this case, we are not given $P(A \cap B)$. Thus, we cannot calculate the exact value of $P(A \cup B)$ without more information. We need $P(A \cap B)$ to complete the calculation.

Part (ខ): When $A$ and $B$ are mutually exclusive (independent events)

When two events $A$ and $B$ are mutually exclusive (independent), the probability of their intersection is: $P(A \cap B) = P(A) \times P(B)$

Therefore, we calculate: $P(A \cap B) = 0.5 \times 0.4 = 0.2$

Now we use the formula for the union of independent events: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ $P(A \cup B) = 0.5 + 0.4 - 0.2 = 0.7$

Summary:

• (ក) When $A$ and $B$ are not mutually exclusive: We need $P(A \cap B)$ to calculate $P(A \cup B)$.
• (ខ) When $A$ and $B$ are mutually exclusive (independent): $P(A \cup B) = 0.7$

Would you like more details on any specific part, or do you have any questions?

Related Questions:

1. How do you calculate the probability of the union of two dependent events?
2. What is the difference between mutually exclusive and independent events?
3. How do you determine if two events are independent or dependent?
4. What is the probability of the intersection of two events?
5. How do you use Venn diagrams to solve probability problems?
6. What is the addition rule in probability?
7. Can you explain the concept of conditional probability?
8. How does the law of total probability work in probability theory?

Tip:

Always ensure to understand the relationship between events (whether they are independent or dependent) before applying the relevant probability rules.