The vaccination

The vaccination coverage of the population is 80%. Unvaccinated make up 60% of all infected. What percentage are unvaccinated and more likely to be infected? Consider N = 10,000 inhabitants and K = 1,000 infected.

b. How many times more likely are unvaccinated?

Correct answer:

p =  25 %
b =  6

Step-by-step explanation:

$$\begin{gathered} N=10000 \\ K=1000 \\ o=0.80\cdot N=0.80\cdot 10000=8000 \\ n=(1-0.8)\cdot N=(1-0.8)\cdot 10000=2000 \\ nn=0.60\cdot K=0.60\cdot 1000=600 \\ no=(1-0.6)\cdot K=(1-0.6)\cdot 1000=400 \\ {p}_1=100\cdot \frac{nn}{n}=100\cdot \frac{600}{2000}=\frac{100\cdot 600}{2000}=\frac{60000}{2000}=30\% \\ {p}_2=100\cdot \frac{no}{o}=100\cdot \frac{400}{8000}=\frac{100\cdot 400}{8000}=\frac{40000}{8000}=5\% \\ p=p_1-p_2=30-5=25\% \end{gathered}$$

$b=\frac{p_1}{p_2}=\frac{30}{5}=6$

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