A fair cube with faces numbered from 1 through 6 is tossed a number of times. If the probability of the cube landing on the number 2 every time is 1/216, what is the best answer for how many times the cube is rolled?

Question

anonymous · Answer

If your cube is "fair" that means it has an equal probability of coming up on any side--specifically the probability that it comes up on 2--is 1/6. 

The probability of it coming up on 2 the first time is 1/6. The probability of that happening on the first AND the second time is 1/6*1/6 = 1/36. The probability of it coming up on 2 for n independent trials in a row is 1/6n. So we have 

1/6n = 1/216
6n = 216
n = 36