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,D_3` is

Explanation

Required Probablity =`(.^6C_1 * 1/6*1/6* 5/6 * 5/6).^3C_1 + (.^6C_1*1/6*1/6*1/6*5/6).^3C_2 + .^6C_1*1/6*1/6*1/6*1/6`

=`1/6^3[3 xx 25 + 3 xx 5 + 1]`

`= 1/216[75+ 15+1]`

`= 91/216`

option A is correct