The vaccination

The vaccination coverage of the population is 80%. Unvaccinated make up 60% of all infected. What percentage are unvaccinated more likely to be infected?

Correct answer:

p =  40 %

Step-by-step explanation:

$$\begin{gathered} o=80\mathrm{\%}={\displaystyle \frac{80}{100}}=0.8 \\ n=1-o=1-0.8={\displaystyle \frac{1}{5}}=0.2 \\ nn=0.60\cdot n=0.60\cdot 0.2={\displaystyle \frac{3}{25}}=0.12 \\ no=o\cdot (1-0.6)=0.8\cdot (1-0.6)={\displaystyle \frac{8}{25}}=0.32 \\ zo=o\cdot 0.6=0.8\cdot 0.6={\displaystyle \frac{12}{25}}=0.48 \\ zn=n\cdot (1-0.6)=0.2\cdot (1-0.6)={\displaystyle \frac{2}{25}}=0.08 \\ p=100\cdot (zo-zn)=100\cdot (0.48-0.08)=40=40\mathrm{\%} \\ \text{ Verifying Solution: } \\ t=nn+no+zo+zn=0.12+0.32+0.48+0.08=1 \end{gathered}$$

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