The faces on a regular octahedral die are numbered one through eight. What is the probability of rolling 3 sixes in succession? Express your answer as a common fraction.

what is the probability of rolling a six (i.e. __ out of eight)? cube that value to get the probability of rolling 3 sixes in succession

To find the probability of rolling 3 sixes in succession on an octahedral die, we need to determine two things: the total number of possible outcomes and the number of favorable outcomes.

In this case, the total number of possible outcomes can be found by considering that we roll the die three times, and there are 8 possible numbers on each roll. Therefore, the total number of outcomes is 8 * 8 * 8 = 512.

Next, we need to determine the number of favorable outcomes, which is the number of ways we can roll three sixes in succession. Since each roll is independent, the probability of rolling a six on a single roll is 1/8. So the number of favorable outcomes is 1/8 * 1/8 * 1/8 = 1/512.

Therefore, the probability of rolling 3 sixes in succession is 1/512, which is the ratio of the number of favorable outcomes to the total number of possible outcomes.

It's important to note that the probability can also be expressed as a decimal or a percentage. In this case, 1/512 is approximately 0.001953125 or about 0.195%.