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 $${E^c}$$ denote the complement of an event $$E.$$ Let $$E, F, G$$ be pairwise independent events with $$P\left( G \right) > 0$$ and $$P\left( {E \cap F \cap G} \right) = 0.$$ Then $$P\left( {{E^c} \cap {F^c}|G} \right)$$ equals

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 $${u_i}$$ be the event of selecting ith urn, $$i=1,2,3........,n$$ and $$w$$ the event of getting a white ball.

Let $$P\left( {{u_i}} \right) = {1 \over n},$$ if $$n$$ is even and $$E$$ denotes the event of choosing even numbered urn, then the value of $$P\left( {w/E} \right)$$ is

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 $${u_i}$$ be the event of selecting ith urn, $$i=1,2,3........,n$$ and $$w$$ the event of getting a white ball.

If $$P\left( {{u_i}} \right) = c,$$ (a constant) then $$P\left( {{u_n}/w} \right) = $$