A and B are independent events. P(A) = 0.40 and P(B) = 0.30. What is P(A and B)?A.0.70B.0.12C.0.012D.0SUBMITarrow_backPREVIOUS

1. Break Down the Problem

To find the probability of independent events A and B occurring together (denoted as P(A and B)), we can use the formula for independent events:

$P(A \text{ and } B) = P(A) \times P(B)$

2. Relevant Concepts

Since A and B are independent events, the joint probability is simply the product of their individual probabilities.

3. Analysis and Detail

Given:

• $P(A) = 0.40$
• $P(B) = 0.30$

Now, we will substitute these values into the formula:

$P(A \text{ and } B) = P(A) \times P(B) = 0.40 \times 0.30$

4. Verify and Summarize

Calculating the product:

$P(A \text{ and } B) = 0.40 \times 0.30 = 0.12$

This result indicates that the joint probability of both events A and B occurring is 0.12.

Final Answer

The correct answer is B. 0.12.