Events A and B have P(A) = 0.4, P(B) = 0.5, P(A \cap B) = 0.2. Are A and B independent?

Yes — P(A) \cdot P(B) = 0.20 = P(A \cap B) Independence: P(A∩B) = P(A)P(B) = 0.4·0.5 = 0.2 ✓. Mutually exclusive would mean P(A∩B) = 0, which is different.

Yes — A and B are mutually exclusive

Yes — P(A) \cdot P(B) = 0.20 = P(A \cap B)

No — they cannot be independent if both occur

Cannot be determined without more data

Conditional Probability

AP Statistics· difficulty 4/5

P(A) = 0.4

A
$Yes — A and B are mutually exclusive$
B
$P(A) \cdot P(B) = 0.20 = P(A \cap B)$
check_circle
C
$No — they cannot be independent if both occur$
D
$Cannot be determined without more data$

Explanation

Independence: P(A\capB) = P(A)P(B) = 0.4\cdot0.5 = 0.2 ✓. Mutually exclusive would mean P(A\capB) = 0, which is different.

Want 10 more like this — adaptive to your weak spots?

Practice 10 like thisarrow_forward Predict my AP score

Related questions