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..
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..