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AP EAMCET201921 Apr 2019Morning ShiftMathematicsProbabilityActual

A and B each select one number at random from the distinct numbers 1,2,3, , n and the probability that the number selected by A is less than the number selected by B is 1009 2019 . Now, the probability that the number selected by B is the number immediately next to the number selected by A is

Options

  1. A2018 2019
  2. B2018 (2019)^2
  3. C2000 (2019)
  4. D2000 (2019)^2

Correct answer

B. 2018 (2019)^2

Step-by-step solution

It is given that, A and B each select one number at random from the distinct numbers 1,2 , 3, , n , then the probability that the number selected by A is less than the number selected by B is array rlrl & & ^n C₂ n n & = n(n-1) 2(n n) = 1009 2019 (given) n-1 2 n & = 1009 2019 2019 n-2019=2018 n n & =2019 array Now, number of ways selecting numbers from the distinct numbers 1,2,3, , 2019 , by B is the number immediately next to the number selected by A is 2018 , because there are 2018 pairs of consecutive numbers. S

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