A student mixes \(50.0\text{ mL}\) of \(1.6 \times 10^{-5}\text{ M }\text{Ba(NO}_3\text{)}_2\text{(aq)}\) with \(50.0\text{ mL}\) of \(1.0 \times 10^{-5}\text{ M }\text{Na}_2\text{SO}_4\text{(aq)}\) at \(25\text{ }^\circ\text{C}\). The dissolution equilibrium for barium sulfate is represented by the following equation.

\[\text{BaSO}_4\text{(s)} \rightleftharpoons \text{Ba}^{2+}\text{(aq)} + \text{SO}_4^{2-}\text{(aq)} \quad\quad K_{sp} = 1.0 \times 10^{-10} \text{ at } 25\text{ }^\circ\text{C}\]

Which of the following correctly predicts whether a precipitate of \(\text{BaSO}_4\text{(s)}\) will form and provides the correct justification?