Multiple choice

Two dice were thrown simultaneously. Then find the probability of g etting at least one outcome as multiple of 3.

  1. $\dfrac{2}{9}$
  2. $\dfrac{1}{6}$
  3. $\dfrac{5}{12}$
  4. $\dfrac{5}{9}$
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D Correct answer
Explanation

Probability of at least one multiple of 3 = 1 - P(no multiple of 3). Multiples of 3 on a die are 3, 6 (2 outcomes). Non-multiples are 1, 2, 4, 5 (4 outcomes). P(no multiple) = (4/6) * (4/6) = 16/36 = 4/9. P(at least one) = 1 - 4/9 = 5/9.

AI explanation

A multiple of 3 on a die can be either a 3 or a 6, giving a probability of 2/6, or 1/3, for one die to show a multiple of 3. The probability of not getting a multiple of 3 on a single die is 2/3, making the probability of not getting a multiple of 3 on either die (2/3) times (2/3), which equals 4/9. The probability of getting at least one multiple of 3 is 1 minus the probability of getting none, calculated as 1 minus 4/9. This leaves a final probability of 5/9.

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