Question

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An unbiased dice with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum value is not less than 2 and the maximum value is not
greater than 5 is:
a) 1/81 b) 80/81
c) 16/81 d) 65/81

Solution with some explanation

Answer 1

Step-by-step explanation:

Let us intepret this condition in our context:

"...that the minimum value is not less than 2 and the maximum value is not greater than 5"

This means that when we roll the dice, we do not want 1 or 6 to appear. Instead we wish for 2/3/4/5 to appear.

The probability of getting these four sides out of six in a roll is 4/6, or 2/3.

We have to roll this dice 4 times. Hence we raise the probability to a power of 4:

Total probability = (2/3)⁴

= (2)⁴ / (3)⁴

= 16/81. (C)