A boss decides to distribute Rs. 2000 between 2 employees. He knows X deserves…

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A boss decides to distribute Rs. 2000 between 2 employees. He knows X deserves more that Y, but does not know how much more. So he decides to arbitrarily break Rs. 2000 into two parts and give X the bigger part. What is the chance that X gets twice as much as Y or more?

  1. A.

    2/5

  2. B.

    1/2

  3. C.

    1/3

  4. D.

    2/3

Attempted by 12 students.

Show answer & explanation

Correct answer: D

Key idea: treat the larger share given to X as a uniform variable between 1000 and 2000.

  • Let X denote the larger share given to the employee X. Because the boss gives the larger part to X, X can be any amount between 1000 and 2000 with equal likelihood.

  • The smaller share is Y = 2000 − X. The condition we need is X ≥ 2Y.

  • Substitute Y: X ≥ 2(2000 − X) ⇒ X ≥ 4000/3 ≈ 1333.33.

  • Favourable values of X are from 4000/3 up to 2000. The length of this interval is 2000 − 4000/3 = 2000/3.

  • Total possible values of X span 1000 (from 1000 to 2000). Thus the probability is (2000/3) / 1000 = 2/3.

Answer: 2/3

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