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A coin is tossed. If head appears a fair...

A coin is tossed. If head appears a fair die is thrown three times otherwise a biased die with probability of obtaining an even number twice as that of an odd number is thrown three times. If `(n_(1),n_(2),n_(3))` is an outcome, `(1 le n_(1) le6)` and is found to satisfy the equation `i^(n_(1))+i^(n_(2))+i^(n_(3))=1`, , then the probability that a fair die was thrown is (where `i=sqrt(-1))`

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