probability

Question

1 Indian and 4 american man and their wives are to be seated along the circular table.what is the conditional probability that the Indian man is seated adjacent to his wife. Given that each american man is seated adjacent to his wife.

Answer 1

Seat the 4 American couples (in such a way each American man is seated adjacent to his wife).

Seat the Indian man. Then there are 5 ways to seat his wife (numbers 1 to 5 in the figure).

In that, 1 and 2 are favorable cases(because, in these cases, Indian man is seated adjacent to his wife).

Therefore, required probability $=\frac{2}{5}$

 

Answer 2

Let E = event when each American man is seated adjacent to his wife..

A = event when Indian man is seated adjacent to his wife

Now, n(A ∩ E) = (4!)×(2!)^5

Even when each American man is seated adjacent to his wife Again n(E) =(5!)×(2!)^4   

     P(A/E)=(n(A∩E))/n(E)

                 =(4!)×(2!)^5/(5!)×(2!)^4

                 =2/5.

Alternative Fixing four American couples and one Indian man in between any two couples; we have 5 different ways in which his wife can be seated, of which 2 cases are favorable.

∴ required probability = 2/5