Multiple choice

Two die are thrown. Find the probability that t he number on the upper face of the first dice is less than the number on the upper face of the second dice.

  1. $\displaystyle \frac{1}{2}$
  2. $\displaystyle \frac{7}{12}$
  3. $\displaystyle \frac{1}{3}$
  4. $\displaystyle \frac{5}{12}$
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D Correct answer
Explanation

There are 36 equally likely ordered outcomes when two dice are thrown. Six outcomes have equal numbers, and the remaining 30 split equally between the first die being larger and the first die being smaller. Thus, the required probability is 15/36 = 5/12.

AI explanation

When two dice are thrown, the total number of outcomes in the sample space is 6 times 6, which equals 36. The condition requires the first die to be strictly less than the second, which occurs for the pairs (1,2), (1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6), (3,4), (3,5), (3,6), (4,5), (4,6), and (5,6), giving exactly 15 favorable outcomes. Using the classical probability formula, the probability is 15 divided by 36, which simplifies to 5/12.

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