Multiple choice

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is less than seven?

  1. $\dfrac 5{12}$
  2. $\dfrac 7{12}$
  3. $\dfrac 1{12}$

  4. None of these
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A Correct answer
Explanation

There are 36 total outcomes when rolling two dice. The sums less than seven are 2 (1,1), 3 (1,2; 2,1), 4 (1,3; 3,1; 2,2), 5 (1,4; 4,1; 2,3; 3,2), and 6 (1,5; 5,1; 2,4; 4,2; 3,3), totaling 15 outcomes. The probability is 15/36, which simplifies to 5/12.

AI explanation

When two dice are thrown, the total number of possible outcomes is 36. The outcomes where the sum is less than seven are (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (4,1), (4,2), and (5,1), totaling 15 combinations. Using the classical definition of probability, the required probability is the ratio of favorable outcomes to total outcomes, which is 15/36 = 5/12.

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