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KVPY2020MathematicsProbability

In a regular 15 - sided polygon with all its diagonals drawn, a diagonal is chosen at random. The probability that it is either a shortest diagonal nor a longest diagonal is

Options

  1. A2 3
  2. B5 6
  3. C8 9
  4. D9 10

Correct answer

A. 2 3

Step-by-step solution

Total diagonals = C 2 15 - 15 = 90 Shortest diagonal = Diagonal connecting A 1 A 3 , A 2 A 4 , … = 15 longest diagonal = Diagonal connecting A 1 A 8 , A 1 A 9 , … = 15 Required probability = 90 - 15 - 15 90 = 60 90 = 2 3

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