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MHT CET20226 Aug 2022Morning ShiftMathematicsProbabilityActual

Let be a complex cube root of unity with 1 . A fair die is thrown three times. If r₁, r₂ and r₃ are the numbers obtained on the die, then the probability that ^ r₁ + ^ r₂ + ^ r₃ =0 , is

Options

  1. A1 36
  2. B1 8
  3. C1 9
  4. D2 9

Correct answer

D. 2 9

Step-by-step solution

Solution: aligned & ^ r₁ + ^ r₂ + ^ r₃ =0 & each of r₁, r₂, r₃ belongs to each of the categories 3 k, 3 k+1, & 3 k+2 aligned So the required probability 3 1 3 1 3 1 3 = 2 9

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