One Indian and four American men and their wi | vedclass

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Question

(C) Let $E$ be the event that each American man is seated adjacent to his wife.Let $A$ be the event that the Indian man is seated adjacent to his wife

Vedclass · Accepted Answer

$2 / 5$

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(C) Let $E$ be the event that each American man is seated adjacent to his wife.Let $A$ be the event that the Indian man is seated adjacent to his wife.Total number of people is $10$ ($5$ men and $5$ wives).When each American couple is seated together,we treat each of the $4$ American couples as a single unit. Including the Indian man and his wife,we have $6$ units to arrange around a circular table.However,the condition is that each American man is seated adjacent to his wife. There are $4$ such couples. Let us treat each couple as a block. There are $4$ such blocks and $2$ individuals (Indian man and his wife). Total $6$ entities to arrange in a circle: $(6-1)! = 5!$ ways. Each of the $4$ American couples can be arranged in $2!$ ways. So,$n(E) = 5! 	imes (2!)^4$.Now,for $n(A \cap E)$,the Indian couple is also seated together. We treat the Indian couple as a block. Now we have $5$ blocks ($4$ American couples + $1$ Indian couple) to arrange in a circle: $(5-1)! = 4!$ ways. Each of the $5$ couples can be arranged in $2!$ ways. So,$n(A \cap E) = 4! 	imes (2!)^5$.The conditional probability is $P(A|E) = \frac{n(A \cap E)}{n(E)} = \frac{4! 	imes (2!)^5}{5! 	imes (2!)^4} = \frac{4! 	imes 2}{5!} = \frac{2}{5}$.

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

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