# Complex Probability

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

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