What is the probability that the ‘person is actually having COVID given that ‘he is tested as COVID positive’?

0.083

Let,

E: The event that person selected has COVID.

F: The event that person selected does not have COVID.

G: The event that person is tested positive.

$P\left(\frac{\text{tested covid}}{\text{has covid}}\right)=P(\frac{G}{E})=90\%$

$=0.9$

$P\left(\frac{\text{tested covid positive}}{\text{does not have covid}}\right)=1\%=0.01$

$\text{person not having covid}=1-P(person covid)$

$P(F)=1-P(E)$

$=1-0.001=0.999$

$P\left(\frac{\text{having covid}}{\text{covid positive}}\right)=P(\frac{E}{G})$

$=\frac{P(E).P(G|E)}{P(E)P(G|E)+P(F)P(G|F)}$

$=\frac{0.001×0.9}{0.001×0.9+0.999×0.01}$

$=0.083$

$\text{P(person selected will be diagnosed as covid positive)} = P(F)×P(G|F)+P(E)P(G|E)$

$=0.001×0.9+0.999×0.01$

$=0.01089$