JEE Advanced · Mathematics · 32. Probability
Paragraph:
There are \(n\) urns each containing \((n+1)\) balls such that the ith urn contains \(i\) white balls and \((n+1-i)\) red balls. Let \(u_i\) be the event of selecting ith urn, \(i=1,2,3, \ldots, n\) and \(W\) denotes the event of getting a white balls.Question:
If \(n\) is even and \(E\) denotes the event of choosing even numbered urn \(\left(P\left(u_i\right)=\frac{1}{n}\right)\), then the value of \(P(W / E)\) is
- A
\(\frac{n+2}{2 n+1}\)
- B
\(\frac{n+2}{2(n+1)}\)
- C
\(\frac{n}{n+1}\)
- D
\(\frac{1}{n+1}\)
Answer & Solution
Correct Answer
(B)
\(\frac{n+2}{2(n+1)}\)
Step-by-step Solution
Detailed explanation
\(P(W / E)=\frac{2+4+6+\ldots}{\frac{n(n+1)}{2}}=\frac{n+2}{2(n+1)}\)
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