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GATE 2019 ME (ME1) – Question 38

Engineering Mathematics · Probability and Statistics: Probability, conditional probability, sampling theorems · 2 marks · Multiple choice

Variables x and y are uniformly distributed on 0 to 10 and 0 to 20 respectively. Find the probability x + y > 20.

  1. 0
  2. 0.25
  3. 0.33
  4. 0.50

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Correct answer: (B) 0.25

Explanation

Assuming independence, the joint density is $1/(10\cdot20)$. The region $x+y>20$ is a triangle with base 10 and height 10. Thus probability is $(10\cdot10/2)/200=\mathbf{0.25}$, **B**. Independence is implicit in the official answer; uniform marginals alone do not specify the joint distribution.