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`        Let w be a complex cube root of unity,w is not equal to 1.A fair die is thrown three times.If r1,r2 and r3 are the numbers obtained on the die,then the probability that w^r1+w^r2+w^r3=0 is?`
6 months ago

```							w^1 + w^2 + w^3 = 0 w^1 = w^4 w^2 = w^5 1 = w^3 = w^6 Probability that r1 = 1 or 4, r2 = 2 or 5, r3 = 3 or 6 = 2/6 * 2/6 * 2/6 = 1/27 If the values of r1, r2, r3 are reshuffled, then also we will get w^r1 + w^r2 + w^r3 = 0 The values of r1, r2, r3 can be reshuffled in 3! = 6 wats Therefore, the required probability = 6 * 1/27 = 2/9 Ans: 2/9
```
6 months ago
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