Four fair dice , `D_1 D_2, D_3 and D_4` each having six faces numbered 1,2,3,4,5 and 6 are rolled simultaneously. The probability that `D_4` shows a number appearing on one of `D_1,D_2 and D_3` is

Options

A. `(91)/(216)`
B. `(108)/(216)`
C. `(125)/(216)`
D. `(127)/(216)`

Answer

A

Explanation

Required probability
=1-Probability that number on `D_(4)` is different from number on `D_(1),D_(2) " and " D_(3)`
`=1-((.^(6)C_(1)xx5^(3))/(6^(4)))=1-(125)/(216)=(91)/(216)`