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JEE Main202229 Jul 2022Morning ShiftMathematicsProbabilityActual

Let S = 1 , 2 , 3 , … , 2022 . Then the probability, that a randomly chosen number n from the set S such that H C F n , 2022 = 1 , is

Options

  1. A128 1011
  2. B166 1011
  3. C127 337
  4. D112 337

Correct answer

D. 112 337

Step-by-step solution

Given, S = 1 , 2 , 3 , … , 2022 So, total number of elements = 2022 Now factors of 2022 = 2 × 3 × 337 Now HCF n , 2022 = 1 is feasible only when the value of ' n ' and 2022 has no common factor. Now let A = Number which are divisible by 2 from 1 , 2 , 3 , . . . 2022 So, n A = 1011 Now let B = Number which are divisible by 3 by 3 from 1 , 2 , 3 , . . . 2022 So, n B = 674 Now A ∩ B = Number which are divisible by 6 Now from 1 , 2 , 3 , . . . 2022 number multiple of 6 are 6 , 12 , 18 , .

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