Probability

There are \(n\) urns each containing \(n+1\) balls such that the \(i^{\text {th }}\) urn contains \(i\) white balls and \((n+1-i)\) red balls. Let \(u_{i}\) be the event of selecting \(i^{\text {th }}\) urn, \(i =1,2,3 \ldots, n\) and \(w\) denotes the event of getting a white ball.

If \(n\) is even and E denotes the event of choosing even numbered urn \(\left(\mathrm{P}\left(u_{i}\right)=\frac{1}{n}\right)\),
then the value of \(\mathrm{P}(w / \mathrm{E})\) is :