ProbabilityHard
Question
One Indian and four American men and their wives are to be seated randomly around a circular table. Then 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
Options
A.1/2
B.1/3
C.2/5
D.1/5
Solution
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
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 =
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
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 =
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