Multiple choice

Three dice are thrown simultaneously. Find the probability of getting the same number on all the three dice.

  1. $\dfrac{1}{36}$  
  2. $\dfrac{1}{3}$  
  3. $\dfrac{5}{36}$  

  4. None of these
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A Correct answer
Explanation

When three dice are thrown, there are 6*6*6 = 216 total outcomes. The outcomes where all three dice show the same number are (1,1,1), (2,2,2), (3,3,3), (4,4,4), (5,5,5), and (6,6,6), which is 6 outcomes. Probability = 6/216 = 1/36.

AI explanation

When three dice are thrown, the total number of possible outcomes in the sample space is 6 times 6 times 6, which equals 216. Getting the same number on all three dice means rolling either three 1s, three 2s, three 3s, three 4s, three 5s, or three 6s, giving exactly 6 favorable outcomes. The required probability is the number of favorable outcomes divided by the total outcomes, which is 6/216, simplifying to 1/36.

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