Question

which of the following is not true about conditional probability?
a. p(a | b) is independent of event b.
b. p(a) = p(a | b)
c. p(a | b) is the probability of event a given that event b has already occurred.
d. p(a | b) is the probability of event a occurring before event b.

Explanation:

Conditional probability $P(A|B)$ is the probability of event $A$ given event $B$ has occurred. It is dependent on event $B$. Also, $P(A) = P(A|B)$ only when $A$ and $B$ are independent. And $P(A|B)$ is not the probability of $A$ occurring before $B$.

Answer:

A. $P(A | B)$ is independent of event $B$.
B. $P(A)=P(A | B)$
D. $P(A | B)$ is the probability of event $A$ occurring before event $B$.