Let be a complex cube root of unity with 1 . A fair die is thrown three times. If r₁, r₂ and r₃ are the numbers obtained on the die, then the probability that ^ r₁ + ^ r₂ + ^ r₃ =0 is

Step-by-step solution

Sample space A dice is thrown thrice, n(s)=6 6 6 . Favorable events ^ r₁ + ^ r₂ + ^ r₃ =0 ie, (r₁, r₂, r₃ ) are ordered 3-triples which can take values, . array llll (1,2,3), & (1,5,3), & (4,2,3), & (4,5,3) (1,2,6), & (1,5,6), & (4,2,6), & (4,5,6) array ie, 8 ordered pairs and each can be arranged in 3 ! ways =6 array ll & n(E)=8 6 & P(E)= 8 6 6 6 6 = 2 9 array