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Let be a complex cube root of unity with {1}. A fair die is t

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Let $ω$ be a complex cube root of unity with $ω \neq = 1$ . 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 $ω^{r_{1}} + ω^{r_{2}} + ω^{r_{3}} = 0$ is

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James Discussed

Let

ω

be a complex cube root of unity with

ω \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

ω^{r_{1}} + ω^{r_{2}} + ω^{r_{3}} = 0

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Question Text

Let

ω

be a complex cube root of unity with

ω \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

ω^{r_{1}} + ω^{r_{2}} + ω^{r_{3}} = 0

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