Assertion -For any two events A and B- P A- B - P B -P A- B - Reason- A- B and A- B are mutually exclusive events-

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Byju's Answer

Standard XII

Mathematics

Intersection of Sets

Assertion :Fo...

Question

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.

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
Since $A \cap B a n d ¯ A \cap B$ are mutually exclusive
$∴ (A \cap B) \cup (¯ A \cap B) = B$
$∴ P [(A \cap B) \cup (¯ A \cap B)] = P (B)$
$\Rightarrow P (A \cap B) + P (¯ A \cap B) = P (B)$
$\Rightarrow P (¯ A \cap B) = P (B) - P (A \cap B)$
Hence Assertion (A) followed by Reason (R).

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Assertion :For any two events A and B, P(¯A∩B)=P(B)−P(A∩B). Reason: A∩B and ¯A∩B are mutually exclusive events.

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.