If P(A) = 0.4 and P(B) = 0.5, what is P(A and B) if events A and B are independent?

• A. 0.1
• B. 0.2
• C. 0.4
• D. 0.5

Answer: (B)

When dealing with independent events in probability, the probability of both events occurring is calculated by multiplying their individual probabilities. In this scenario, you have events A and B with probabilities P(A) = 0.4 and P(B) = 0.5, respectively.

Since A and B are independent, the probability of both A and B happening simultaneously, denoted as P(A and B), can be found using the formula:

P(A and B) = P(A) × P(B)

Substituting the given values into the formula:

P(A and B) = 0.4 × 0.5

This calculation results in:

P(A and B) = 0.2

Therefore, the correct probability of both independent events A and B occurring together is 0.2. This demonstrates the principle of independence in probability, where the occurrence of one event does not affect the occurrence of another.