Question

If P(A) = .50, P(B) = .30, and P(A ∩ B) = .15, then A and B are independent events.

True or False

Answer 1

true

Explanation:

To determine if events A and B are independent, we can use the definition of independent events:

Two events, A and B, are independent if and only if:

P(A ∩ B) = P(A) × P(B)

In this case, you've provided:

P(A) = 0.50

P(B) = 0.30

P(A ∩ B) = 0.15

Now, let's check if the equation holds:

P(A ∩ B) = P(A) × P(B)

0.15 = 0.50 × 0.30

0.15 = 0.15

Since the equation holds true, A and B are indeed independent events. So, the statement is True.