# Abrazolica

Probability of Meeting Someone with COVID-19

Currently in Colorado (where we live) about 1 person in 50 has COVID-19. So let $p=1/50$ be the probability that when you meet someone in Colorado, they have COVID-19.

The premise behind this assumption is that you have an equal probability of being exposed to everyone in the population. This is generally not true. People tend to confine themselves to subpopulations, and the probability of COVID-19 in different subpopulations can vary greatly. We just want to do a simple analysis so we'll assume it's true.

So the question is, if you come into contact with $n$ people, what is the probability that at least one of them has COVID-19? The probability that none of them has it is $(1-p)^n$ therefore the probability that at least one of them has it is

$1-(1-p)^n$

The value of $n$ for which this is at least $0.5$, i.e. you have an even chance of contacting someone with COVID-19 is

$n=-\log(2)/\log(1-p)$

The average number of people you have to come into contact with to meet someone with COVID-19 is $1/p$. For Colorado right now this is $50$.
Below is a plot of the probability of meeting someone with COVID-19 as a function of $n$ given that $p=1/50$.
Probability of contacting someone with COVID-19 as a function of $n$ given that $p=1/50$