Question

Let a and b be independent events with p(a) = 0.40 and p(b) = 0.50. What is the probability of both events occurring?

1) 0.20
2) 0.40
3) 0.50
4) 0.70

Answer 1

The probability of two independent events a and b occurring simultaneously is calculated by multiplying their individual probabilities, which results in 0.20.

Step-by-step explanation:

Since a and b are independent events, the probability of both events occurring is found by multiplying their individual probabilities. The probability of event a occurring is 0.40, and the probability of event b occurring is 0.50. Therefore, the probability of both a and b occurring is:

P(a AND b) = P(a) × P(b) = 0.40 × 0.50 = 0.20.

The correct answer to the probability of both independent events a and b occurring is 0.20, which corresponds to option 1) 0.20.