A) \[\frac{7}{64}\]
B) \[\frac{9}{64}\]
C) \[\frac{37}{256}\]
D) \[\frac{39}{256}\]
Correct Answer: B
Solution :
The powers of i contain two sets of numbers that are additive inverses of each other, namely (1, - 1) and (i, -i). Thus the only sets of four numbers that will satisfy a = 0 are permutations of either (1, 1, -1, -1), and (i, -i 1-1). The first two have \[^{4}{{C}_{2}}=6\] distinct arrangement each, while the has 4! = 24 total arrangement, giving 2(6) + 24 = 36 overall. There are \[{{4}^{4}}=256\] possibilities, giving a probability of \[\frac{36}{256}\,=\frac{9}{64}\].
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