Multiple choice

Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is?

  1. 5/9

  2. 5/12

  3. 1/36

  4. 7/12

  5. 4/9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total outcomes = 6^3 = 216. Outcomes with exactly two dice showing the same number: Choose the number that repeats (6 ways), choose the two dice that repeat (3 ways), and choose the number for the third die (5 ways). Total = 6 * 3 * 5 = 90. Probability = 90/216 = 5/12.

AI explanation

When three dice are thrown, the total outcomes are 6 times 6 times 6 for 216. To get exactly two matching numbers, choose the matching value in 6 ways, choose the different value in 5 ways, and arrange the odd die among the three positions in 3C1 ways, giving 6 times 5 times 3 for 90 combinations. The probability is 90 divided by 216, which simplifies to 5/12.

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