The surface of Earth has 5E8 km². They have 1E4 satellites. They are in orbit for a few years, but let's assume all fall down. So you get one satellite per 5E4 km².
There are less than 1E10 humans. 1m² is too big for most humans, perhaps a human and an umbrella. So the surface of humans is less than 1E10 m² = 1E4 km².
With some mild assumptions, I get less that a 20% chance of a satellite hitting a human, assuming all fall down, they can't be aimed at the sea, humans are big, they don't disintegrate in air, and the hit kills the human. How do they get 61%?
The chance that one or more satellites will hit a human 1-x, where x is the chance that none of them will kill a human. x, in turn, is y¹⁰⁰⁰⁰, and y is the fraction of the earth's area where no human is. y¹⁰⁰⁰⁰ because it's the chance that the first satellite doesn't times the chance that the second times...
Raising something to the power of ten thousand makes a difference, even if you start very close to 1. I'm too tired to do the math now, but I bet that's where they get the big number and you don't.
18.127% but my numbers are too rounded so I prefer to round the result to 20% (or at least 18%).
When you have (1-1/A)^B there are two different approximations.
When B > A you can approximate it by e^(-B/A)
When B < A you can approximate it by 1-B/A
The idea is that you can apply the Taylor serie and get (1-1/A)^B = e^(log(1-1/A)B) ~= e^((-1/A-1/A^2)B) ~= e^(-B/A-B/A^2) ~= 1-B/A-B/A^2+(-B/A-B/A^2)^2/2 ~= 1-B/A-B/A^2+B^2/A^2/2 ~= 1-B/A+B^2/A^2/2 dropping that tiny -B/A^2
The thing is that the first part of the approximation B/A is easy to remember. And the first correction is (B/A)^2*something, but I never remember that something is just 1/2, I must redo the calculation when I need it. Usually B/A is fine.
So ... I still don't understand if I made an horrible mistake with my selection of the numbers to make the approximation of they are doing something wrong.
They didn't even mention the danger of evil h4xx0rz taking control of them and targeting specific individuals for space based swats... this time. Someone missed an opportunity.
FFS this click-bait shit is killing me. Starlink is only an example, and likely less likely then all the other low orbit shit flying around up there.
Must the media be so sloppy and shameless?