Question

Which of the following is/are correct if the probability of intersection of two events 'A' and 'B' is zero?

• A. A and B are mutually exclusive.
• B. A and B has one or more common events.
• C. $P(A\cap B)=0$
• D. None of these

Answer 1

Answer: (A), (C)

The correct options are
A A and B are mutually exclusive.
C $P(A\cap B)=0$

Given the probability of intersection of two events $A$ and $B$ is $0$.

That is $P(A\cap B)=0$

We know that when $A$ and $B$ are two mutually exclusive events that is the occurrence of event $A$ does not affect the occurrence of event $B$ at all, in such a case, $P(A\cap B)=0$

Therefore $A$ and $B$ are mutually exclusive events and $P(A\cap B)=0$.

Hence, A and C are correct options.