In developers I've worked with I've observed a lack of understanding of the language/libraries used (ie. the order of something is coincidental, not guaranteed, leading to flakiness) and a lack of understanding of the test system (eg. shared db for multiple test runners, querying last insert is not deterministic in this case) as well as accidental mistakes (tests timeout after 1000ms, enough I/O is in the test that it can vary from 700ms to (rarely) 1200ms.
Recently I wrote a test that checked the deterministic properties of a build. I forgot that the two test builds could run in parallel and thus end up with the same timestamp (to the ms) and thus the same artifact. It never occurs on my dev laptop where it was a single threaded build, but it occurs maybe one in a hundred times on my desktop. Simple to fix, but easy to write. The fix was of course to mock the timestamp properly.
Sometimes organizational imperatives like code coverage goals can result in less-than-stellar tests. Sometimes a developer doesn't understand the system well enough, and sometimes (often, in my experience) something outside the logical scope of a test changes, e.g., an underlying implicit dependency.
Even a test that is 100% reliable today may become unreliable tomorrow.
Now you run multiple tests, each with a more complex environment than your real system (you need to control your tests, test logs etc.) usually on a lesser environment than your production one. Add all this and you'll get an uncomfortable probability of failure
Minor nitpick: when probabilities multiply, they get smaller. Such is the nature of numbers in the range [0, 1].
Multiplication would happen when counting the probability of two (independent) events coinciding. What you're thinking about here is the probability of any one of several events occuring. That will be a (rather convoluted) sum, not a product.