A fair dice is thrown three times. If p, q and r are the numbers obtained on the dice, then find the probability that `i^(p) + i^(q) + i^(r) = 1`, whe

Question

A fair dice is thrown three times. If p, q and r are the numbers obtained on the dice, then find the probability that `i^(p) + i^(q) + i^(r) = 1`, whe

A fair dice is thrown three times. If p, q and r are the numbers obtained on the dice, then find the probability that `i^(p) + i^(q) + i^(r) = 1`, where `I = sqrt(-1)`.

Monjur Alahi

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2025-01-04 04:42

1 Answers

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

Salim Ahmed Kawsar

The possbile values of p, q and r are (1, 3, 4), (3, 4, 5), (4, 4, 6) and (2, 4, 4) not in order.
`therefore` Number of favourable cases = `3! + 3! + 3 + 3= 18`
Total number of cases = `6 xx 6 xx 6`
`therefore` Required probability = `(18)/(216) = (1)/(12)`

6 views Answered 2023-02-05 15:29