Independent and identically distributed (IID) means that the probability distribution of each variable in a set of random variables is the same, and these random variables are independent of each other.

The fact that a set of random variables are independent and identically distributed does not mean that the probability of each event in their sample space is the same. For example, the sequence of results obtained by rolling uneven dice is independent and identically distributed, but the probability of rolling each face up is not the same.

References

【1】Wikipedia: Independent and identically distributed