Assertion (A): If P (A/B) = P (B/A ). A, B are two non. M.E. events then P(A ) = P(B). Reason (R): For non mutually exclusive events A ∩ B ≠ φ and P(A/B) = (P(A ∩ B)/P(B)), P(B /A) = (P(A ∩ B)/P(A)).

Question

Assertion (A): If P (A/B) = P (B/A ). A, B are two non. M.E. events then P(A ) = P(B). Reason (R): For non mutually exclusive events A ∩ B ≠ φ and P(A/B) = (P(A ∩ B)/P(B)), P(B /A) = (P(A ∩ B)/P(A)). (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.

Tardigrade Admin · Accepted Answer

P(A/B) = P(B/A) ⇒ (P(A ∩ B)/P(B)) = (P(B∩ A)/P(A)) ⇒ P(A) = P(B) ⇒ Assertion (A) follows by Reason (R).

Q. Assertion (A) : If $P (A / B) = P (B / A) . A, B$ are two non. M.E. events then $P (A) = P (B)$ .
Reason (R) : For non mutually exclusive events $A \cap B \neq = ϕ$ and $P (A / B) = \frac{P ( A \cap B )}{P ( B )}$ ,
$P (B / A) = \frac{P ( A \cap B )}{P ( A )}$ .

Both (A) & (R) are individually true & (R) is correct explanation of (A).

Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).

(A) is true but (R) is false.

(A) is false but (R) is true.

$P (A / B) = P (B / A)$
$\Rightarrow \frac{P ( A \cap B )}{P ( B )} = \frac{P ( B \cap A )}{P ( A )}$
$\Rightarrow P (A) = P (B)$
$\Rightarrow$ Assertion (A) follows by Reason (R).

Q. Assertion (A) : If P(A/B)=P(B/A).A,B are two non. M.E. events then P(A)=P(B). Reason (R) : For non mutually exclusive events A∩B=ϕ and P(A/B)=P(B)P(A∩B)​, P(B/A)=P(A)P(A∩B)​.