JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Probability

Let E = event that each American man is seated adjacent to his wife, and A = event that the Indian man is seated adjacent to his wife.

Given that each American couple sits together, we can treat each couple as a unit. There are 4 American couples and 1 Indian man, making 5 units to arrange in a circle.

For event E: $n(E)=(5!)\times (2!{)}^4$ (5 units in a circle, each American couple can swap positions)

For event $A\cap E$: Treat the Indian couple also as a unit, so 5 units total: $n(A\cap E)=(4!)\times (2!{)}^5$

Therefore, $P(A|E)=\frac{n(A\cap E)}{n(E)}=\frac{(4!)\times (2!{)}^5}{(5!)\times (2!{)}^4}=\frac{2}{5}$.