NOVAD-26 Virus

The test is 99% sensitive and 99% specific. That is, the test will produce 99% true positive results for infected humans, and 99% true negative results for non-infected humans.

Also, it is known that the number of infected humans is 8∙10^5.
Let us denote the following events:

$I$ - Infected

$\lnot I$ - Not infected

$T$ - Positive test

$\lnot T$ - Negative test

$D$ - Died

World population today is approximately $8\cdot 10^9$ .

We can use this fact to estimate the prior probability for a human to be infected as follows:

$P(I)=\frac{8\cdot 10^5}{8\cdot 10^9}=0.0001$

Now we can find the probability to be infected given that the test gave positive result using Baye’s theorem as follows:

$P\left(I\middle| T\right)=\frac{P\left(T\middle| I\right)\cdot P\left(I\right)}{P\left(T\right)}$

$=\ \frac{P\left(T\middle| I\right)\cdot P\left(I\right)}{P\left(T\middle| I\right)\cdot P\left(I\right)+P\left(T\middle|\lnot I\right)\cdot P\left(\lnot I\right)}$

$=\frac{0.99\cdot 0.0001}{0.99\cdot 0.0001+0.01\cdot 0.9999}\cong0.0098$

The probability to die is than,

$P\left(D\middle| I\right)\cdot P(I|T)=0.02\cdot0.0098=0.000196$

So even though the test gave a positive result, the chances for you to be infected are less than 1% and the chances that you will die by the virus are less than 0.02%.