Question

Determine if events
P(A) = 0.4
P(B) = 0.5
P( A ∩ B) = 0.18
are independent or dependent.
(1 Point)

Dependent

Independent

Answer 1

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

\[ P(A ∩ B) = P(A) \cdot P(B) \]

Given:
- \( P(A) = 0.4 \)
- \( P(B) = 0.5 \)
- \( P(A ∩ B) = 0.18 \)

Now, calculate \( P(A) \cdot P(B) \):

\[
P(A) \cdot P(B) = 0.4 \cdot 0.5 = 0.2
\]

Now, compare this with \( P(A ∩ B) \):

\[
P(A ∩ B) = 0.18
\]

Since \( P(A ∩ B) (0.18) \) is not equal to \( P(A) \cdot P(B) (0.2) \), we conclude that the events A and B are **dependent**.

So, the answer is **Dependent**.