A 'die' indicates one, 'dice' indicates two or more.
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Die is the singular form whereas dice is plural. If I have 1 I have a die yet if I had more I would have some dice. Just like in mouse and mice or in man and men.
A fair die is a die where the probability of throwing each of the faces is equal. Dice is two or more die's.
The probability for dice depends on how many. For a die, it is 1/3.
A fair die (fair dice) is a dice which isn't altered in any way, this means it has the same chance of landing on any of one of the faces. The opposite to this is a loaded dice or cheat dice. These dice have been altered in some way, maybe by changing the weight distribution so that one of the numbers on the die/dice are more likely to be rolled.
Throw is a very large number of times. If the six numbers come up approximately 1/6 number of times then it is likely that the die (not dice!) is fair. If one or more numbers comes up more often than the die is not fair. You can never be certain.