Question

Assertion (A) : If the independent events $A\& B$ are such that $0 < P\left(A\right) < 1, 0 < P\left(B\right) < 1$ then events $A\& B$ can not be mutually exclusive.
Reason (R) : Two events $A\& B$ can not be mutually exclusive if $P\left(A \cap B\right) \ne0$.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A).
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Answer 1

Answer: (A)

Since $A\&B$ are independent
$\therefore P\left(A \cap B\right)=P\left(A\right)P\left(B\right)\ne0$
As $0 < P\left(A\right) < 1 0 < P\left(B\right) < 1$
$\Rightarrow $ events $A\& B$ can not be mutually exclusive. $\left(\because P\left(A \cap B\right)\ne0\right)$