When rolling 3 standard number cubes, the probability of getting all three numbers to match is 6216. What is the probability that the three numbers do not all match? Explain your reasoning.

Question

When rolling 3 standard number cubes, the probability of getting all three numbers to match is 6216. What is the probability that the three numbers do not all match? Explain your reasoning.

Answer 1

It looks like you meant to type 6/216. This makes sense because in rolling 3 six-sided dice, there are 6³ possible outcomes, or 216. Of those 216, only 6 have all 3 numbers matching (111, 222, 333, 444, 555, 666). This 6/216 figure actually reduces to 1/36.

The probability that they do not all match is the probability that you don't get this outcome, or the probability that you get any outcome other than this one. That would mean 1 - 1/36, which is 35/36, or 0.972222.