Mathematics - Probability Question with Solution | TestHub

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, $i=1,2,3,\dots ,n$ and $W$ denotes the event of getting a white balls.Question:If $P\left(u_i\right)\propto i$, where $i=1,2,3,\dots ,n$, then ${\lim }_{n\to \infty }P(W)$ is equal to