Multiple choice

Four dice are rolled, then the probability that at least one digit on the dice must be repeated is

  1. $\dfrac{1}{18}$
  2. $\dfrac{13}{18}$
  3. $\dfrac{5}{18}$
  4. $\dfrac{1}{9}$
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B Correct answer
Explanation

The total outcomes for 4 dice is 6^4 = 1296. The number of ways to have no repeated digits is 6 * 5 * 4 * 3 = 360. The probability of no repetition is 360/1296 = 5/18. The probability of at least one repetition is 1 - 5/18 = 13/18.

AI explanation

Use the complementary event method, where the probability of at least one repeat equals 1 minus the probability of all four digits being different. The total outcomes when rolling four dice are 6^4 = 1296, and the favorable outcomes for all different digits are 6 x 5 x 4 x 3 = 360. The probability of no repeats is 360 / 1296 = 5/18, so the probability of at least one repeat is 1 - 5/18 = 13/18.

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