If two fair dices are thrown and digits on dices are a and b, then find the probability for which `omega^(ab) = 1`, (where `omega` is a cube root of u

Question

If two fair dices are thrown and digits on dices are a and b, then find the probability for which `omega^(ab) = 1`, (where `omega` is a cube root of u

If two fair dices are thrown and digits on dices are a and b, then find the probability for which `omega^(ab) = 1`, (where `omega` is a cube root of unity).

Monjur Alahi

7 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - `(5)/(9)`
Total number of cases n(S) = 36
Since `omega^(ab)` = 1, ab must be multiple of 3.
So, at least one of a and b must be multiple of 3.
If none of the dices shows 3 or 6, number of cases is `4 xx 4 = 16`.
So, number of cases in which at least one of the dices shows 3 or 6 is 36 - 16 = 20.
`therefore` Required probability = `(20)/(36) = (5)/(9)`