One Indian and four American men and their wives are to be seated randomly around a circular table. 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

$\frac{2}{5}$

Let A denote the event that each American man is seated adjacent to his wife and B denote the event that Indian man is seated adjacent to his wife. Then,

Required probability = P(B/A)

Number of ways in which Indian man sits adjacent to his wife when each man is seated adjacents

$=\frac{\text{to his wife}}{\text{Number of ways in which each American man is seated adjacent to his wife}}$

$=\frac{(2!)^5×(5-1)!}{(2!)^4(6-1)!}=\frac{2}{5}$