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KVPY2012MathematicsProbability

Let S _ n = _ k =1 ^ n k denote the sum of the first n positive integers. The numbers S ₁, ~S ₂, ~S ₃, S ₉₉ are written on 99 cards. The probability of drawing a card with an even number written on it is -

Options

  1. A1 / 2
  2. B49 / 100
  3. C49 / 99
  4. D48 / 99

Correct answer

C. 49 / 99

Step-by-step solution

1,3,6,10,15,21,28,36,45,55,66,78,91,105 till 98 terms 48 terms are even and 48 terms odd 99^ th term = 99 100 2 = even Total even terms =48+1=49 Probability = 49 99

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