Let A and B be two disjoint events such that P(A) = 0.20 and P(B) = 0.60.What is P(A and B)? 0 0.12 0.68 0.80

1. Break Down the Problem

We need to find the probability of two disjoint events A and B occurring at the same time, denoted as $P(A \text{ and } B)$.

2. Relevant Concepts

For two disjoint (or mutually exclusive) events, the probability of both events occurring simultaneously is given by: $P(A \text{ and } B) = 0$ This is because disjoint events cannot happen at the same time.

3. Analysis and Detail

Given that $P(A) = 0.20$ and $P(B) = 0.60$, we can analyze the implications:

• Since events A and B are disjoint, they do not overlap; hence the occurrence of one event completely excludes the possibility of the other occurring.

4. Verify and Summarize

Verifying our understanding of disjoint events, we confirm that: $P(A \text{ and } B) = 0$

Final Answer

Thus, the probability $P(A \text{ and } B)$ is $0$.