Multiple choice

Six faces of an unbiased die are numbered with $2, 3, 5, 7, 11$ and $13$. If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number is

  1. $\dfrac5{18}$
  2. $\dfrac5{36}$
  3. $\dfrac{13}{18}$
  4. $\dfrac{25}{36}$
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A Correct answer
Explanation

The faces are {2, 3, 5, 7, 11, 13}. There are 5 odd numbers and 1 even number. Sum is odd if one die is even and the other is odd. Probability = (P(E)*P(O) + P(O)*P(E)) = (1/6 * 5/6) + (5/6 * 1/6) = 5/36 + 5/36 = 10/36 = 5/18.

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