Maths · Probability: Probability of an event, addition and multiplication theorems of probability
Assertion For any two events and =\boldsymbol{P}(\boldsymbol{B})-\boldsymbol{P}(
Assertion For any two events \( A \) and \( B \) \( \boldsymbol{P}(\overline{\boldsymbol{A}} \cap \boldsymbol{B})=\boldsymbol{P}(\boldsymbol{B})-\boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \) Reason \( A \cap B \) and \( \bar{A} \cap B \) are mutually exclusive events.
- 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
Step-by-step solution
The assertion is true because P(B) = P(A ∩ B) + P(Ā ∩ B) since A and Ā are disjoint, so P(Ā ∩ B) = P(B) - P(A ∩ B). The reason states that A ∩ B and Ā ∩ B are mutually exclusive, which is true and directly leads to the assertion. Hence both are true and reason correctly explains assertion.
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