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### Given:
- \( P(A) = 0.6 \)
- \( P(B) = 0.3 \)
- \( A \) and \( B \) are mutually exclusive events, meaning \( P(A \cap B) = 0 \).

Now let's solve each part:

---

**a) \( P(A \text{ and } B) \)**

Since \( A \) and \( B \) are mutually exclusive events, the probability of both events occurring at the same time is zero:
\[
P(A \cap B) = 0
\]

---

**b) \( P(A \text{ or } B) \)**

For mutually exclusive events, the probability of either \( A \) or \( B \) occurring is the sum of their individual probabilities:
\[
P(A \cup B) = P(A) + P(B)
\]
Substitute the given values:
\[
P(A \cup B) = 0.6 + 0.3 = 0.9
\]

---

**c) \( P(\text{not } A) \)**

The probability of the complement of \( A \) (i.e., "not \( A \)") is:
\[
P(\text{not } A) = 1 - P(A)
\]
Substitute the value for \( P(A) \):
\[
P(\text{not } A) = 1 - 0.6 = 0.4
\]

---

**d) \( P(\text{not } B) \)**

Similarly, the probability of the complement of \( B \) (i.e., "not \( B \)") is:
\[
P(\text{not } B) = 1 - P(B)
\]
Substitute the value for \( P(B) \):
\[
P(\text{not } B) = 1 - 0.3 = 0.7
\]

---

### Final Answers:
- a) \( P(A \text{ and } B) = 0 \)
- b) \( P(A \text{ or } B) = 0.9 \)
- c) \( P(\text{not } A) = 0.4 \)
- d) \( P(\text{not } B) = 0.7 \)

Would you like any further clarification or details?

### Relative Questions:
1. What is the definition of mutually exclusive events?
2. How would the calculations change if \( A \) and \( B \) were not mutually exclusive?
3. How do mutually exclusive events differ from independent events?
4. Can two mutually exclusive events ever be independent?
5. What happens to \( P(A \cup B) \) if the events are independent?

### Tip:
Always check if events are mutually exclusive or independent before applying probability formulas, as different rules apply!

If A and B are two mutually exclusive events with P(A) = 0.6 and P(B) = 0.3, find the following probabilities: a) P(A and B) b) P(A or B) c) P(not A) d) P(not B)

Find the probability of mutually exclusive events A and B, where P(A) = 0.6 and P(B) = 0.3. The solution covers P(A and B), P(A or B), P(not A), and P(not B) using key probability concepts and formulas. Suitable for students in Grades 9-12.

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