Question

Suppose A and B are events in a sample space S and suppose that P(A) = 0.6, P(Bc) = 0.4, and P(A ∩ B) = 0.2. What is P(A ∪ B)?

Answer 1

The probability of event A occurring, event B occurring, or both events occurring is 1.0.

Step-by-step explanation:

We can find P(A ∪ B) using the formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Given that P(A) = 0.6, P(Bc) = 0.4 (which implies that P(B) = 1 - 0.4 = 0.6), and P(A ∩ B) = 0.2, we substitute the values into the formula:

P(A ∪ B) = 0.6 + 0.6 - 0.2 = 1.0

Therefore, the probability of either event A or event B occurring, or both events occurring, is 1.0.