There are n urns, each of these contain n+1 balls. The ith urn contains i white balls and n+1−i red balls. Let ui be the event of selecting ith urn, i=1,2,3,⋯n and w be the event of getting a white ball.If P(ui)∝i, where i=1,2,3⋯n, then limn→∞P(w) equals to

There are n urns, each of these contain n+1 balls. The ith urn contain

1.	There are n urns, each of these contain n+1 balls. The ith urn contains i white balls and n+1−i red balls. Let ui be the event of selecting ith urn, i=1,2,3,⋯n and w be the event of getting a white ball.If P(ui)∝i, where i=1,2,3⋯n, then limn→∞P(w) equals to
Answer» There are $n$ urns, each of these contain $n + 1$ balls. The $i^{t h}$ urn contains $i$ white balls and $n + 1 - i$ red balls. Let $u_{i}$ be the event of selecting $i^{t h}$ urn, $i = 1, 2, 3, \dots n$ and $w$ be the event of getting a white ball. If $P (u_{i}) \propto i$ , where $i = 1, 2, 3 \dots n,$ then $lim n \to \infty P (w)$ equals to