# Complex Probability

**Discrete Mathematics**Level 3

Let \(\omega\) be a complex cube root of unity with \(\omega \neq 1\) .A fair die is thrown three times. If \(r_1\) , \(r_2\) and \(r_3\) are the numbers obtained on the die, then the probability that is \(\omega^{r_1} + \omega^{r_2} + \omega^{r_3} = 0\) is