Multiple choice

A fair dice is rolled three times, then the probability of getting a number larger than the previous number is

  1. $\cfrac { 5 }{ 216 } $
  2. $\cfrac { 5 }{ 54 } $
  3. $\cfrac { 1 }{ 6 } $
  4. $\cfrac { 5 }{ 36 } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total outcomes = 6^3 = 216. Favorable outcomes (x < y < z): Choose 3 distinct numbers from 6, which is 6C3 = 20. Probability = 20/216 = 5/54.

AI explanation

The total number of outcomes when rolling a die three times is 6^3, which is 216. The number of ways to get three strictly increasing numbers is the number of ways to choose 3 distinct numbers from 6, calculated as 6C3, which equals 20. Using the classical probability formula, the probability is 20/216, which simplifies to 5/54. The answer is 5/54.

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