Assertion :If $P (A / B) = P (B / A)$ . A, B are two non mutually exclusive events then $P (A) = P (B)$ . Reason: 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 Assertion & Reason are individually true & Reason is correct explanation of Assertion

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

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Assertion is true but Reason is false

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Assertion is false but Reason is true

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Solution

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
We know,
For non mutually exclusive events, $P (A / B) = \frac{P (A . B)}{P (B)}, P (B / A) = \frac{P (A . B)}{P (A)}$
Given $P (A / B) = P (B / A)$
Hence $P (A) = P (B)$

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Similar questions

Q. Assertion : Two events A and B are such that

P (A) = \frac{1}{3}

and

P (B) = \frac{2}{3}

then

P (A \cup B) \geq \frac{2}{3}

Reason : If

P (B) > P (A)

, then

P (A \cup B) \geq P (B)

Assertion : In rolling a die, event A = {1, 3, 5} and event B = {2, 4} are mutually exclusive events.
Reason : In a sample space two events are mutually exclusive if they do not occur at the same time.

Assertion: In rolling a dice, event A = {1, 3, 5} and event B = {2, 4} are mutually exclusive events.
Reason: In a sample space, two events are mutually exclusive if they do not occur at the same time.

Q. Assertion :If A, B, C are three events such that

P (A) = \frac{1}{4}

P (B) = \frac{1}{6}

P (C) = \frac{2}{3}

then events A, B, C are mutually exclusive. Reason: If

P (A \cup B \cup C) = P (A) + P (B) + P (C)

then A, B, C are mutually exclusive events.

Q. Assertion :For any two events A and B,

P (¯ A \cap B) = P (B) - P (A \cap B)

. Reason:

A \cap B

and

¯ A \cap B

are mutually exclusive events.

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Assertion :If P(A/B)=P(B/A). A, B are two non mutually exclusive events then P(A)=P(B). Reason: 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).

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of AssertionWe know, For non mutually exclusive events, P(A/B)=P(A.B)P(B),P(B/A)=P(A.B)P(A)Given P(A/B)=P(B/A)Hence P(A)=P(B)

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

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
We know,
For non mutually exclusive events, $P (A / B) = \frac{P (A . B)}{P (B)}, P (B / A) = \frac{P (A . B)}{P (A)}$
Given $P (A / B) = P (B / A)$
Hence $P (A) = P (B)$