Q

# Need clarity, kindly explain! 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 seat

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

• Option 1)

$\frac{1}{2}$

• Option 2)

$\frac{1}{3}$

• Option 3)

$\frac{2}{5}$

• Option 4)

$\frac{1}{5}$

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As we learned

Conditional Probability -

Let A and B be any two events such that $\dpi{80} B\neq \phi$  or

n(B) = 0 or P(B) = 0 then $\dpi{100} P\left ( \frac{A}{B} \right )$ denotes the conditional probability of occurrence of event A when B has already occured

-

$P\left ( \frac{l_{M}l_{W}}{A_{M}A_{W}} \right )$ $=\frac{4!\cdot (2!)^{5}}{5!\cdot (2!)^{4}}=\frac{2}{5}$

Option 1)

$\frac{1}{2}$

Option 2)

$\frac{1}{3}$

Option 3)

$\frac{2}{5}$

Option 4)

$\frac{1}{5}$

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