One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

Let H$$_1$$, H$$_2$$, ..., H$$_n$$ be mutually exclusive and exhaustive events with P(H$$_i$$) > 0, i = 1, 2, ..., n. Let E be any other event with 0 < P(E) < 1.

Statement 1 : P(H$$_i$$ | E) > P(E | H$$_i$$). P(H$$_i$$) for $$i=1,2,...,n$$.

Statement 2 : $$\sum\limits_{i = 1}^n {P({H_i}) = 1} $$.

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 $$\mathrm{P}\left(u_{i}\right) \propto i$$, where $$i=1,2,3, \ldots n$$, then $$\lim_\limits{n \rightarrow \infty} \mathrm{P}(w)$$ is equal to: