Assertion If are two events such that =\frac{2}{5}, P(B)=\frac{3}{4} \) then \leq \frac{2}{5} \) Reason \leq \max \{\boldsymbol{P}(\boldsymbol{A}), \boldsymbol{P}(B)\} \& \) \geq \min \{\boldsymbol{P}(\boldsymbol{A}), \boldsymbol{P}(\boldsymbol{B})\} \)

Assertion is true but Reason is false

Maths · Probability: Probability of an event, addition and multiplication theorems of probability

Assertion If are two events such that =\frac{2}{5}, P(B)=\frac{3}{4} \) then \le

Assertion If \( A \& B \) are two events such that \( P(A)=\frac{2}{5}, P(B)=\frac{3}{4} \) then \( \frac{1}{20} \leq \) \( P(A \cap B) \leq \frac{2}{5} \) Reason \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \leq \max \{\boldsymbol{P}(\boldsymbol{A}), \boldsymbol{P}(B)\} \& \) \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \geq \min \{\boldsymbol{P}(\boldsymbol{A}), \boldsymbol{P}(\boldsymbol{B})\} \)

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

Step-by-step solution

Assertion: Given P(A)=2/5, P(B)=3/4. For any two events, we have P(A∩B) ≤ min(P(A),P(B))=2/5, and P(A∩B) ≥ max(0, P(A)+P(B)-1)=3/20. Since 1/20 < 3/20, the inequality 1/20 ≤ P(A∩B) holds, so the Assertion is true. Reason: The correct inequalities are P(A∪B) ≥ max(P(A),P(B)) and P(A∩B) ≤ min(P(A),P(B)). The Reason states the opposite, making it false. Hence Assertion true, Reason false.

Practise more in this unit View MCQs Sign up for full question bank

Step-by-step solution

Related MCQs