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.