Given below are two statements. One is labelled as Assertion and the other is labelled as…
Mathematics · JEE Main · NTA Exams — Statistics and Probability
STATEMENT - 1 (Assertion): Let \(E_{i}(i=1,2, \ldots n)\) be n independent events such that \(P\left[\bar{E}_{i}\right]=\frac{i}{i+1}\) , 1 ≤ i ≤ n, the probability that none of the n events occur is equal to \(\frac{n}{n+1}\).
STATEMENT - 2 (Reason): If the events \(E_{1}, E_{2}, E_{3}, \ldots, E_{n}\)are independent then \(P\left[E_{1} \cap E_{2} \cap E_{3} \ldots \cap E_{n}\right]=P\left[E_{1}\right] \cdot P\left[E_{2}\right] \ldots P\left[E_{n}\right]\).
- Both Assertion and Reason are true and Reason is the correct explanation of Assertion
- Both assertion and Reason are true but Reason is not the correct explanation of Assertion
- Assertion is true and Reason is false
- Assertion is false and Reason is true
Answer
(D) Assertion is false and Reason is true
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