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\begin{aligned} P P V & = Pr (Y = 1 | D = 1) = \frac{Pr (Y = 1) Pr (D = 1 | Y = 1)}{Pr (D = 1 | Y = 2) + Pr (Y = 1) [Pr (D = 1 | Y = 1) - Pr (D = 1 | Y = 2)]} \\ N P V & = Pr (Y = 2 | D = 2) = \frac{[1 - Pr (D = 1 | Y = 2)] [1 - Pr (Y = 1)]}{1 - Pr (D = 1 | Y = 2) - Pr (Y = 1) [Pr (D = 1 | Y = 1) - Pr (D = 1 | Y = 2)]} \\ P C & = Pr (Y = 1 | D = 1) + Pr (Y = 2 | D = 2) \\ = Pr (D = 1 | Y = 1) Pr (Y = 1) + Pr (D = 2 | Y = 2) [1 - Pr (Y = 1)] \end{aligned}

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\begin{align*} \textnormal{PPV} & = {\Pr }(Y\! =\! 1|D\! =\! 1) = \frac{{\Pr }(Y\! =\! 1){\Pr }(D\! =\! 1|Y\! =\! 1)}{{\Pr }(D\! =\! 1|Y\! =\! 2) + {\Pr }(Y\! =\! 1)[{\Pr }(D\! =\! 1|Y\! =\! 1) - {\Pr }(D\! =\! 1|Y\! =\! 2)]} \\ \textnormal{NPV} & = {\Pr }(Y\! =\! 2|D\! =\! 2) = \frac{[1-{\Pr }(D\! =\! 1|Y\! =\! 2)]{[1-\Pr }(Y\! =\! 1)]}{1-{\Pr }(D\! =\! 1|Y\! =\! 2) - {\Pr }(Y\! =\! 1)[{\Pr }(D\! =\! 1|Y\! =\! 1) - {\Pr }(D\! =\! 1|Y\! =\! 2)]} \\ \textnormal{PC} & = {\Pr }(Y\! =\! 1|D\! =\! 1) + {\Pr }(Y\! =\! 2|D\! =\! 2) \\ & = {\Pr }(D\! =\! 1|Y\! =\! 1){\Pr }(Y\! =\! 1)+{\Pr }(D\! =\! 2|Y\! =\! 2)[1-{\Pr }(Y\! =\! 1)] \\ \end{align*}