TS EAMCET · Maths · Probability
If \(A_i(i=1,2,3, \ldots, n)\) are \(n\) independent events with \(P\left(A_i\right)=\frac{1}{1+i}\) for each \(i\), then the probability that none of \(A_i\) occurs is
- A \(\frac{n-1}{n+1}\)
- B \(\frac{n}{n+1}\)
- C \(\frac{n}{n+2}\)
- D \(\frac{1}{n+1}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{n+1}\)
Step-by-step Solution
Detailed explanation
The required probability \(=P\left(\bar{A}_1 \cap \bar{A}_2 \cap \ldots \cap \bar{A}_n\right)\) \(=P\left(\bar{A}_1\right) P\left(\bar{A}_2\right) \ldots P\left(\bar{A}_n\right)\) \(=\frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \ldots \cdot \frac{n}{n+1}\) \(=\frac{1}{n+1}\)
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