Multiple choice

Two dice each with faces marked $1,2,3,4,5,6$ are thrown simultaneously. Find the probability of the following events: (i) The sum of the numbers coming up $7$. (ii) The sum of the numbers coming up is a multiple of $4$.

  1. $(i)\displaystyle \frac{1}{6},(ii)\frac { 1 }{ 4 } $
  2. $(i)\displaystyle \frac{1}{3},(ii)\frac { 2 }{ 9 } $
  3. $(i)\displaystyle \frac{5}{6},(ii)\frac { 1 }{ 9 } $

  4. None of these
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A Correct answer
Explanation

(i) Sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes. Prob = 6/36 = 1/6. (ii) Sum is multiple of 4 (4, 8, 12): (1,3), (3,1), (2,2), (2,6), (6,2), (3,5), (5,3), (4,4), (6,6) = 9 outcomes. Prob = 9/36 = 1/4.

AI explanation

When two dice are thrown, the total number of outcomes is 36. The favorable outcomes for getting a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1), giving a probability of 6/36 or 1/6. For the sum to be a multiple of 4 (4, 8, or 12), the favorable outcomes are 3 for sum 4, 5 for sum 8, and 1 for sum 12, totaling 9 outcomes; thus, the probability is 9/36 or 1/4. The resulting probabilities are 1/6 and 1/4.

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