1. គេឲ្យ A និង B ជាព្រឹត្តិការណ៍ 2 ដែល : 
P(A) = 0.5 , P(B) = 0.4 ។ 
គណនា P(A U B) ក្នុងករណី : 
ក. A និង B មិនចុះសម្រុងគ្នា ( ទាក់ទងគ្នា) ។ 
ខ. A និង B មិនទាក់ទងគ្នា។ 
Please tell me

To solve for \( P(A \cup B) \), we need to understand the two cases given:

1. \( A \) and \( B \) are dependent (related).
2. \( A \) and \( B \) are independent (unrelated).

Let's use the given probabilities:
- \( P(A) = 0.5 \)
- \( P(B) = 0.4 \)

### Case 1: \( A \) and \( B \) are Dependent (Related)
For dependent events, we use the general formula for the union of two events:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

However, without additional information about \( P(A \cap B) \), we can't find a specific numeric value for \( P(A \cup B) \). Thus, the formula remains:
\[ P(A \cup B) = 0.5 + 0.4 - P(A \cap B) \]
\[ P(A \cup B) = 0.9 - P(A \cap B) \]

### Case 2: \( A \) and \( B \) are Independent (Unrelated)
For independent events, \( P(A \cap B) \) is the product of their individual probabilities:
\[ P(A \cap B) = P(A) \times P(B) \]
\[ P(A \cap B) = 0.5 \times 0.4 = 0.2 \]

Now, applying the formula for the union of two events:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
\[ P(A \cup B) = 0.5 + 0.4 - 0.2 \]
\[ P(A \cup B) = 0.7 \]

### Summary:
- For dependent (related) events: \( P(A \cup B) = 0.9 - P(A \cap B) \)
- For independent (unrelated) events: \( P(A \cup B) = 0.7 \)

Would you like further details or have any questions?

### Related Questions:
1. What is the general formula for the probability of the union of two events?
2. How do you calculate the probability of the intersection of two independent events?
3. What is the definition of independent events in probability theory?
4. How do dependent events differ from independent events?
5. Can the probability of an intersection \( P(A \cap B) \) be greater than the probability of the union \( P(A \cup B) \)?
6. How do you interpret \( P(A \cup B) \) in a real-world context?
7. What happens to \( P(A \cup B) \) if \( P(A \cap B) = 0 \)?
8. Why do we subtract \( P(A \cap B) \) when calculating \( P(A \cup B) \)?

### Tip:
When dealing with probability problems, carefully determine whether events are independent or dependent, as this will significantly affect the calculations and final results.

Explore how to calculate the probability of the union of events A and B with detailed examples. Learn about dependent and independent events in probability theory. Suitable for high school students studying probability.

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