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A fair dice is thrown three times. If p,...

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)`.

Text Solution

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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)`
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