Probability 3 Question 11

11. One Indian and four American men and their wives are to be seated 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) 12

(b) 13

(c) 25

(d) 15

(2007, 3M)

Show Answer

Solution:

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

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

Now,

n(AE)=(4!)×(2!)5

Even when each American man is seated adjacent to his wife.

 Again, n(E)=(5!)×(2!)4PAE=n(AE)n(E)=(4!)×(2!)5(5!)×(2!)4=25

Alternate Solution

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 favourable.

Required probability =25



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