A student mixes \(100.0\text{ mL}\) of \(2.0 \times 10^{-3}\text{ M }\text{Pb(NO}_3)_2\text{(aq)}\) with \(100.0\text{ mL}\) of \(4.0 \times 10^{-3}\text{ M }\text{NaI(aq)}\) at \(25^\circ\text{C}\). The value of \(K_{sp}\) for \(\text{PbI}_2\) at this temperature is \(1.0 \times 10^{-8}\). Which of the following correctly predicts whether a precipitate of \(\text{PbI}_2\text{(s)}\) will form and provides the valid justification?