Multiple choice

Three identical dice are thrown. (i) What is the probability of getting a total of $15$? (ii) What is the probability that an odd number is obtained on each die given that the sum obtained is $15$ ?

  1. $\displaystyle \frac{5}{108}$, $\displaystyle \frac{1}{10}$
  2. $\displaystyle \frac{5}{108}$, $\displaystyle \frac{3}{10}$
  3. $\displaystyle \frac{5}{54}$, $\displaystyle \frac{3}{10}$

  4. none of these
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A Correct answer
Explanation

Total outcomes = 6^3 = 216. Sum of 15: (6,6,3)x3, (6,5,4)x6, (5,5,5)x1 = 10 outcomes. Prob = 10/216 = 5/108. For (ii), odd numbers summing to 15: (5,5,5) is 1 way. Total odd-sum combinations: (5,5,5) is the only one. Prob = 1/10.

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