Questionbank: Permutation and Probability

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    Q.20: 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. 2/5
    2. 1/2
    3. 1/3
    4. 2/3


  • Correct Answer
    Choice D. 2/3

Explanatory Answer

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Detailed Solution

The bigger part could be any number from 1000 to 2000.

Now, if the bigger part is to be at least twice as much as the smaller part, we have

X ≥ 2Y or X ≥ 2(2000 – X)

Or X ≥ 4000/3

Given that X lies between 1000 and 2000, what is the probability that X lies between 4000/3 and 2000?

This probability is equal to (2000 − 4000/3)/(2000 − 1000) = 2/3

Answer choice (d).

Correct Answer : 2/3

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