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Question
If the sum of the ordinate and the abscissa of a point P (x, y) is 2n, where x and y are natural numbers, then probability that the point does not lie on y = x is:
If the sum of the ordinate and the abscissa of a point P (x, y) is 2n, where x and y are natural numbers, then probability that the point does not lie on y = x is:
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Solution
The correct option is B 2n−22n−1
Let x = r, then y = 2n - r.
Then r∈{1,2,........,2n−1}
∴ total number of ways in which x + y = 2n, x, y∈N
are (2n – 1) of which only one point (n, n) lies on the line y = x.
Hence, probability = 2n−22n−1
Let x = r, then y = 2n - r.
Then r∈{1,2,........,2n−1}
∴ total number of ways in which x + y = 2n, x, y∈N
are (2n – 1) of which only one point (n, n) lies on the line y = x.
Hence, probability = 2n−22n−1
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