40% is the probability that a man over the age of 50 has ED, according to the commercial.
You're using the second definition, like gambling odds, 4 to 6 you have ED.
But still you can't use that ratio the way you are using it.
My undergraduate minor was in Math. I've had a lot of statistics and probability, including graduate level.
If you’re still not convinced, ask yourself this.
Is your answer of 66% post covid 3 times more likely than 40% pre covid?
Take a universe of 10 people.
work it out.
If 4 people had it pre-covid, then in what scenario do you get 3x more likely? You can’t.
Either the 40% or the 3x is wrong. because they exceed 100%.
> You’re using the second definition, like gambling odds, 4 to 6 you have ED.
This definition is also the definition that is used in statistics, in scientific literature, etc.
> But still you can’t use that ratio the way you are using it.
Certainly you can. The factor that you multiply the odds by is called the odds ratio. It is given by p0/(1-p0)/[p1/(1-p1)], where p0 and p1 are the probabilities of some event of interest (e.g. the occurance of ED) for the two populations being compared. The odds ratio is very commonly used in research literature in the biological sciences.
> My undergraduate minor was in Math. I’ve had a lot of statistics and probability, including graduate level.
Cool! I got my undergrad degree in math, and also have graduate degrees in math and statistics. I’ve been working as a statistician/data scientist for 20+ years.