AP EAMCET · Maths · Probability
If \(\mathrm{X}_1, \mathrm{X}_2, \ldots \mathrm{X}_{\mathrm{n}}\) are \(\mathrm{n}\) independent events such that \(\mathrm{P}\left(\mathrm{X}_{\mathrm{r}}\right)\) \(=\frac{1}{r+1}, r=1,2, \ldots, n\), then the probability that none of the \(n\) events occur is
- A \(\frac{1}{n}\)
- B \(\frac{1}{n+1}\)
- C \(\frac{\mathrm{n}}{\mathrm{n}+1}\)
- D \(\frac{n+1}{n+2}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{n+1}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{P}\left(\mathrm{X}_1^{\prime} \cap \mathrm{X}_2^{\prime} \cap \mathrm{X}_3^{\prime} \ldots \cap \mathrm{X}_{\mathrm{n}}^{\prime}\right)\)…
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