If $P ( A \mid B ) = 0$ and $P ( A ) \neq 0$, then which statement is false?
A) Events $A$ and $B$ have no sample points in common.
B) Events $A$ and $B$ are dependent.
C) Events $A$ and $B$ are independent.
D) Events $A$ and $B$ are mutually exclusive.

Question

Quizplus · Accepted Answer

C) is false because if $P(A|B) = 0$ and $P(A) \neq 0$, it means that the occurrence of $B$ makes the occurrence of $A$ impossible, indicating that $A$ and $B$ are dependent on each other. Independence would imply $P(A|B) = P(A)$, which contradicts the given condition.

If P(A∣B)=0P ( A \mid B ) = 0P(A∣B)=0 And P(A)≠0P ( A ) \neq 0P(A)=0

If $P ( A \mid B ) = 0$ And $P ( A ) \neq 0$