Multiple choice

An unbiased dice is rolled four times. The probability that the minimum number on any roll is not less than 2 and maximum number on any roll is not greater than 5 is

  1. 16/81

  2. 1/81

  3. 65/81

  4. 80/81
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A Correct answer
Explanation

Each roll has 6 outcomes. The condition 'not less than 2' and 'not greater than 5' means the outcome must be 2, 3, 4, or 5. There are 4 favorable outcomes out of 6 per roll. Probability for one roll = 4/6 = 2/3. For four rolls, probability = (2/3)^4 = 16/81.

AI explanation

The condition that the minimum is not less than 2 and the maximum is not greater than 5 means every roll must result in a 2, 3, 4 or 5. The probability of rolling one of these four numbers on a single die is 4/6 or 2/3. By the multiplication rule for independent events, the probability of this happening on all four rolls is (2/3)^4, which evaluates to 16/81. The probability is 16/81.

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