Question

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

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{2}{5}$
• D. $\frac{1}{5}$

Answer 1

The correct option is C $\frac{2}{5}$

Consider the American couple as single entities. After they are seated, the Indian man can be seated between any two couples.
After fixing the four American couples and the Indian man, there are five positions that his wife can occupy. We have 5 different ways in which his wife can be seated, of which 2 cases are favourable.
$\therefore$ Required probability $=\frac{2}{5}$