Question

When rolling 3 standard number cubes, the probability of getting all three is to match 6/216. What is the probability that the three numbers do not match? Explain reasoning

Answer 1

Answer: 210/216

This reduces to 35/36

I didn't reduce because the given fraction 6/216 wasn't fully reduced either.

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Explanation:

There are 6 faces to one cube. So that's where the first 6 in 6/216 comes from.

The 216 is from the fact that 6*6*6 = 216 representing all the ways to roll 3 dice.

6 of those 216 ways have all three numbers match up, so the remaining 216-6 = 210 ways have the numbers not matching up. We could have all three numbers different, or only two match but the third doesn't match.

So that's why the answer is 210/216. To reduce this, you would divide each part by the GCF 6 to get 35/36. The original fraction 6/216 reduces to 1/36. Notice how 35/36 and 1/36 combine to 36/36 = 1.