An unbiased die with faced marked `1, 2, 3, 4, 5`, and `6` is rolled four times. Out of four face value obtained, the probability that the minimum face value is not less than `2` and the maximum face value is not greater than five is then

Options

A. a) `(16)/(81)`
B. b) `(1)/(81)`
C. c) `(80)/(81)`
D. d) `(65)/(81)`

Explanation

Probability that the minimum face value is not `<2` and the maximum face value not `>5` is:


`P(2` or `3` or `4` or `5 )` `= P(2) + P(3)+ P(4)+P(5) = (1)/(6)+(1)/(6)+(1)/(6)+(1)/(6)`


`P(2` or `3` or `4` or `5` )`=4/6 = 2/3`


Required probability `= 4_(C_4) (2/3)^4(1/3)^0`


`= 1*(2/3)^4*1`


`= 16/81`.