Sorry for the late reply. I’m assuming you need to be “infected” in order to infect someone else (define “infected” so that this is true). Since being infected is a neccessary precondition to infecting someone else,
P(you infect someone else) ⇐ P(you are infected),
and it’s clear you can replace “<=” by “<”.
This is basic probaility theory, I can’t follow your notation but suspect that you are using some different definition of “infected” and/or confusing probabilities with expected values..
That’s the point of the post. Given a large number of contacts, P(infecting at least one of them) > P(you are infected)
Lets illustrate. Suppose P1(you are infected AND (you are asymptomatic OR you are pre-symptomatic))
P2(infecting any one of your contacts) = P2′*P1 = where P2′ is the probability of infection per contact
Then P3(infecting at least one of your contacts out of N) = 1- (1-P2)^N provided none of the N contacts are themselves infected.
And in P3>P1 it is always possible to solve for N.
Sorry for the late reply. I’m assuming you need to be “infected” in order to infect someone else (define “infected” so that this is true). Since being infected is a neccessary precondition to infecting someone else,
P(you infect someone else) ⇐ P(you are infected),
and it’s clear you can replace “<=” by “<”.
This is basic probaility theory, I can’t follow your notation but suspect that you are using some different definition of “infected” and/or confusing probabilities with expected values..