Question

Assertion :If A & B are two events of the same sample space with $P\left(A\right)=P\left(B\right)$ then $P(\overline{A}\cap B)$ can not be determined. Reason: $P(\overline{A}\cap B)=P\left(B\right)-P(A\cap B)$.

• A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
• B. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) 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 & Reason are individually true & Reason is correct explanation of Assertion

Given Assertion :

$\Rightarrow P\left(A\right)=P\left(B\right)$

$\Rightarrow P(A\cap \overline{B})+P(\overline{A}\cap B)=P\left(A\right)+P\left(B\right)-2P(A\cap B)$

$=P(A\cup B)-P(A\cap B)$

$\Rightarrow P(\overline{A}\cap B)=P(A\cup B)-P(A\cap B)-P(\overline{A}\cap B)$

But,$P(\overline{A}\cap B)=P\left(B\right)-P(A\cap B)$ [Reason]

So, if $A$ $\xi$ $B$ are two events with $P\left(A\right)=P\left(B\right),$ but $P(\overline{A}\cap B)$ cannot be determined.

Hence, the answer is Both Assertion and reason are individually true and reason is correct explanation of Assertion.