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GATE 2024 BT – Question 31

Engineering Mathematics · Probability and Statistics: Mean, median, mode, standard deviation, random variables, Poisson, normal and binomial distributions · 1 mark · Multiple choice

The six faces of a cube (die) are numbered as 1, 2, 3, 4, 5 and 6, and it is rolled once. An outcome is the observed number on the top face. If the probability of getting an odd number as an outcome is twice that of an even number, then the probability of getting a number less than 3 is ________.

  1. $\frac19$
  2. $\frac29$
  3. $\frac13$
  4. $\frac49$

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Correct answer: (C) $\frac13$

Explanation

Let each even face have probability $e$ and each odd $2e$ (the probabilities of the faces within each group are equal). Then $3e + 6e = 1$, so $e = \frac19$. $P(1) + P(2) = \frac29 + \frac19 = \frac13$.