Let's solve the problem based on the provided information and image.

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!