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Random phenomenon is a situation in which we dont know what the out come is going to come.

Rolling of unbiased dice is a random phenomenon since we dont know what number is going to come. We can only say every number has 1/6 probability.

Rolling a biased coin on other hand also we dont know which number is going to come. We only know every number does not have 1/6 probability.

So does that mean rolling of biased dice is a random phenomenon ?

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Yes, you are correct. Rolling of dice is (almost always) a random phenomenon. In case of biased v unbiased dice, the difference is solely in the probability distributions. For unbiased the distribution must be uniform, for biased it can be anything we want.

The only case where biased dice stop being random phenomena is when we load them in such a way that they always produce a predetermined number (or a specific sequence).

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