Question

An unbiased die 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 face value is not less than 2 and the maximum face value is not greater than 5 is

1. 16/81
2. 1/81
3. 80/81
4. 65/81

Answer 1

Correct Answer - Option 1 : 16/81

Concept:

Probability of occurring an event = \(\frac {Favourable~outcomes}{Total~outcomes}\)

Calculation:

Given:

Favourable number on die should be  2,3,4,5

When a die is rolled four times, the total number of cases would be, 6 × 6 × 6 × 6

Favourable number of cases = 4 × 4 × 4 × 4

Therefore, the required probability = \(\frac {Favourable~outcomes}{Total~outcomes}\)=\(\frac{4×4×4×4}{6×6×6×6}\) = \(\frac{16}{81}\)