 First of all one would like to reason about cases where more than one object is selected from the domain. Consider for example the probability of first picking a black marble, putting it back, and then picking a white marble from the vase. This probability is 5/9 \(\times\) 4/9 = 20/81, but we cannot express this in the language above. For this we need one operator that deals with multiple variables simultaneously, written as \(Px_1,\ldots x_n (\phi) \geq q\). The semantics for such operators will then have to provide a probability measure on subsets of \(D^n\). The simplest way to do this is by simply taking the product of the probability function \(P\) on \(D\), which can be taken as an extension of \(P\) to tuples, where \(P(d_1,\ldots d_n)= P(d_1) \times \cdots \times P(d_n)\), which yields the following semantics: