12th Class
Mathematics
Sample Paper
Maths Olympiad Model Test Paper-11
question_answer
Let \[\omega \] be a complex cube root of unity with\[\omega \ne 1.\] A fair die is thrown three times. If \[{{n}_{1}},\]\[{{n}_{2}}\] and \[{{n}_{3}}\] are the numbers obtained on the die, then the probability that \[{{\omega }^{{{n}_{1}}}}+{{\omega }^{{{n}_{2}}}}+{{\omega }^{{{n}_{3}}}}=0\] is ________.