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Presumably you are asking what the chance of rolling AT LEAST one 2 is. To do this calculation we first work out the probability of NOT rolling a 2, which is 1/6.

We then calculate the probability of NOT rolling ANY 2 in 500 rolls. That is 1/6 to the power of 500.

So now that we have the probability of it NOT happening, we subtract that number from 1 to get the probability of it happening.

Pr(x) = 1 - 1/6^500

The answer is so close to 1 that it's not worth writing out decimally. Basically 0.999999... with almost 400 nines. It's virtually guaranteed that you will get at least one 2 in 500 rolls.

If your question was instead what is the chance of getting ONLY one 2 out of 500 rolls then the answer is basically the opposite - the answer is almost zero.

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Q: What is the possibility of rolling a 2 out of 500 rolls on a six sided cube?
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