In a finite set Omega of equally likely outcomes, an event A has probability |A|/|Omega|. Choosing independently from finite sets Omega_1,...,Omega_t means every ordered tuple is equally likely. Events restricting distinct coordinates then multiply: if coordinate j must belong to A_j, their joint probability is product_j |A_j|/|Omega_j|. For example, c independent fair bits give 2^c equally likely strings; requiring one specified value at every position leaves fraction 2^{-c}. Repeated values remain different tuple positions. Independence is a property of the sampling rule; events computed from the same sampled object need not be independent.