There are n urns each containing 3n+1 balls such that ith urn contains i white, (i+1) green and (3n–2i) red balls. Let Ui be the event of selecting ith urn, where i=1,2,3,...,n and G denotes the event of getting a green ball. If If P(Ui)∝i2, then limn→∞P(G) is

There are n urns each containing 3n+1 balls such that ith urn contains

1.	There are n urns each containing 3n+1 balls such that ith urn contains i white, (i+1) green and (3n–2i) red balls. Let Ui be the event of selecting ith urn, where i=1,2,3,...,n and G denotes the event of getting a green ball. If If P(Ui)∝i2, then limn→∞P(G) is
Answer» There are $n$ urns each containing $3 n + 1$ balls such that $i^{th}$ urn contains $i$ white, $(i + 1)$ green and $(3 n - 2 i)$ red balls. Let $U_{i}$ be the event of selecting $i^{th}$ urn, where $i = 1, 2, 3, . . ., n$ and $G$ denotes the event of getting a green ball. If If $P (U_{i}) \propto i^{2},$ then $lim n \to \infty P (G)$ is