ProbabilityMedium
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 =
Create a free account to view solution
View Solution FreeMore Probability Questions
A student has to match three historical events i.e. Dandi March, Quit India Movement and Mahatma Gandhi′s assasina...If 4 whole numbers taken at random are multiplied together, then the chance that the last digit in the product is 1, 3, ...The probability of getting number of even numbered outcomes more than number of odd numbered outcomes by throwing a fair...A tetrahedral fair dice whose faces are numbered $1,2,3$ and 4 . The die is thrown and the face on which the pyramid lan...For any two events A & B in a sample space :...