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GATE 2021 ES – Question 37

Mathematics Foundation · Probability and Statistics · 2 marks · Multiple choice

A biased die has faces k=1,…,6 with P(k) proportional to k². Find probability of an even result.

  1. 35/91
  2. 56/91
  3. 12/21
  4. 9/21

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Correct answer: (B) 56/91

Explanation

The normalization is $\sum_{k=1}^6k^2=91$. Even-face weight is 2²+4²+6²=4+16+36=56. Hence probability **56/91,B**. The die is not uniform, so counting three even faces out of six would be incorrect.

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