Social beneficiaries

In a certain community, 52% are SAP beneficiaries, 15% are members of 4Ps, and 8% are both SAP and 4 Ps. If a citizen from the community is an SAP, what is the probability that he is also 4Ps?
If that person is not a 4Ps, what is the probability that he is not an SAP?

SAP = Social Amelioration Program
4P = Pantawid Pamilyang Pilipino Program

Correct answer:

a =  15.3846 %
b =  90.5882 %

Step-by-step explanation:

$$\begin{gathered} SAP=52\%=\frac{52}{100}=\frac{13}{25}=0.52 \\ P=15\%=\frac{15}{100}=\frac{3}{20}=0.15 \\ I=8\%=\frac{8}{100}=\frac{2}{25}=0.08 \\ a=100\cdot \frac{I}{SAP}=100\cdot \frac{\frac{2}{25}}{\frac{13}{25}}=\frac{200}{13}\%=15.3846\% \end{gathered}$$

$$\begin{gathered} NP=1-P=1-\frac{3}{20}=\frac{1\cdot 20}{20}-\frac{3}{20}=\frac{20}{20}-\frac{3}{20}=\frac{20-3}{20}=\frac{17}{20}=0.85 \\ b=100\cdot (1-\frac{I}{NP})=100\cdot (1-\frac{\frac{2}{25}}{\frac{17}{20}})=\frac{1540}{17}\%=90.5882\% \end{gathered}$$

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