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Let's analyze the given information and solve each part of the problem.

Given:
- \( A \) and \( B \) are two **mutually exclusive events**. 
- \( P(A) = 0.43 \)
- \( P(B) = 0.14 \)

Mutually exclusive events mean that both events cannot happen at the same time. Therefore:
\[
P(A \text{ and } B) = 0
\]

### Solving Each Part
#### A. \( P(A \text{ and } B) \)
Since \( A \) and \( B \) are mutually exclusive:
\[
P(A \text{ and } B) = 0
\]

#### B. \( P(A \text{ or } B) \)
The probability of \( A \) or \( B \) (denoted \( P(A \cup B) \)) for mutually exclusive events is given by:
\[
P(A \text{ or } B) = P(A) + P(B)
\]
Substitute the values:
\[
P(A \text{ or } B) = 0.43 + 0.14 = 0.57
\]

#### C. \( P(A^c) \)
\( P(A^c) \) represents the probability of the complement of \( A \), which is \( 1 - P(A) \):
\[
P(A^c) = 1 - 0.43 = 0.57
\]

#### D. \( P(B^c) \)
Similarly, \( P(B^c) \) is the probability of the complement of \( B \):
\[
P(B^c) = 1 - P(B) = 1 - 0.14 = 0.86
\]

### Summary of Answers
- **A.** \( P(A \text{ and } B) = 0 \)
- **B.** \( P(A \text{ or } B) = 0.57 \)
- **C.** \( P(A^c) = 0.57 \)
- **D.** \( P(B^c) = 0.86 \)

Would you like a detailed explanation of any part of this solution? 

### Related Questions
1. What if \( A \) and \( B \) were not mutually exclusive? How would that change the answer?
2. How would you calculate \( P(A \cup B) \) if you knew \( P(A \cap B) \neq 0 \)?
3. What are some real-life examples of mutually exclusive events?
4. How do we interpret the complement of an event in probability?
5. If \( P(A) \) and \( P(B) \) are probabilities of independent events, what would change?

### Tip
When dealing with mutually exclusive events, always remember that the probability of both events happening simultaneously is zero.

Let A and B be two mutually exclusive events. Given that P(A) = 0.43 and P(B) = 0.14, find the following:

A. P(A and B)
B. P(A or B)
C. P(A^c)
D. P(B^c)

Learn how to solve a probability problem involving mutually exclusive events A and B with given probabilities P(A) = 0.43 and P(B) = 0.14. Find P(A and B), P(A or B), P(A^c), and P(B^c) using key probability rules for mutually exclusive events and complements.

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