Question

$A,B$ are two events of a simple space.

Assertion (A):- $A,B$ are mutually exclusive $\Rightarrow P\left(A\right)\le P\left(\overline{B}\right)$

Reason (R):- $A,B$ are mutually exclusive $\Rightarrow P\left(A\right)+P\left(B\right)\le 1$

• A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
• B. Both Assertion and Reason are true and Reason is not the correct explanation of Assertion
• C. Assertion is true but Reason is false
• D. Assertion is false but Reason is true

Answer 1

The correct option is A Both Assertion and Reason are true and Reason is the correct explanation of Assertion

Let the space be consists of only two sets $A$ and $B$.
Then $P\left(A\right)\le P\left(\overline{B}\right)$
$\Rightarrow P\left(A\right)\le 1-P\left(B\right)$
$\Rightarrow P\left(A\right)+P\left(B\right)\le 1$
Hence both the statements are correct and Reason is the correct explanation of Assertion.