Multiple choice

Two symmetrical dice are rolled. The probability that sum of the points on them is divisible by $5$ is

  1. $\dfrac{2}{9}$
  2. $\dfrac{4}{9}$
  3. $\dfrac{7}{36}$
  4. $\dfrac{5}{9}$
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C Correct answer
Explanation

The total outcomes when rolling two dice is 36. Sums divisible by 5 are 5 and 10. Pairs summing to 5 are (1,4), (2,3), (3,2), (4,1) [4 outcomes]. Pairs summing to 10 are (4,6), (5,5), (6,4) [3 outcomes]. Total favorable outcomes = 4 + 3 = 7. Probability = 7/36.

AI explanation

When two symmetrical dice are rolled, the total possible outcomes are 36. The sums divisible by 5 are 5 and 10. The combinations that total 5 are (1,4), (2,3), (3,2), and (4,1), giving 4 outcomes, and the combinations that total 10 are (4,6), (5,5), and (6,4), giving 3 outcomes. The total favorable outcomes are 4 plus 3, which is 7, making the probability 7/36.

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