Denote the pdfs in Exercise 2 by \(f_{1}, f_{2}, f_{3}\), respectively. Suppose that \(X\) is simulated via the two-step procedure: First, draw \(Z\) from \(\{1,2,3\}\), then \(\operatorname{draw} X\) from \(f_{Z}\). How likely is it that the outcome \(x=0.5\) of \(X\) has come from the uniform \(\operatorname{pdf} f_{2}\) ?