Suppose event $A$ and event $B$ are independent. Which of the following is not true?
A) $P(A \cap B) \leq P(A)$
B) $P(A \cap B) \leq P(B)$
C) $P(A \cap B)P(B)$
D) $P(A \cup B) \geq P(B)$

Question

Suppose event $A$ and event $B$ are independent. Which of the following is not true?
A) $P(A \cap B) \leq P(A)$
B) $P(A \cap B) \leq P(B)$
C) $P(A \cap B)>P(B)$
D) $P(A \cup B) \geq P(B)$

Quizplus · Accepted Answer

For independent events $A$ and $B$, $P(A \cap B) = P(A)P(B)$, which cannot be greater than $P(B)$ unless $P(A) > 1$, which is impossible since probabilities cannot exceed 1.

Suppose Event AAA And Event BBB Are Independent P(A∩B)≤P(A)P(A \cap B) \leq P(A)P(A∩B)≤P(A)

Suppose Event $A$ And Event $B$ Are Independent $P(A \cap B) \leq P(A)$