Question

If $P\left(A\right)+P\left(B\right)=1$; then which of the following option explains the event $A$ and $B$ correctly?

• A. Event $A$ and $B$ are mutually exclusive, exhaustive and complementary events
• B. Event $A$ and $B$ are mutually exclusive and exhaustive events
• C. Event $A$ and $B$ are mutually exclusive and complementary events
• D. Event $A$ and $B$ are exhaustive and complementary events

Answer 1

The correct option is A Event $A$ and $B$ are mutually exclusive, exhaustive and complementary events

Mutually exclusive events are those events which cannot happen at the same time.

Mutually exhaustive events are those events in which atleast one of the events should occur.

Atleast one of $A,B$ should happen , both $P\left(A\right),P\left(B\right)$ cannot be zero at same time because given that $P\left(A\right)+P\left(B\right)=1$

Complementary events means those two events are the only possible events.

Here only $A$ and $B$ are possible events because $P\left(A\right)+P\left(B\right)=1$

Therefore Event $A$ and $B$ are mutually exclusive , exhaustive and complementary events.

So the correct option is $A$.