I've been circling around this, but I think the biggest mistake ppl make with statistics is taking a statistic and assuming that it translates to a probability for the individuals it applies to.
EG if 50% if new drivers in the US get into an accident in their first year of driving (a statistic I just made up) and I am a new US driver then I have a 50% chance or getting in an accident ie: there's essentially a coin toss to determine whether or not I'll get in an accident this year.
Statistics are about populations and they don't translate to the individual level like that. An abstract new US driver has a 50% chance according to my made up statistic but whether or not an individual gets into an accident is the result of causal forces. How do you drive, how much do you drive, what do you drive, where do you drive, how good are you at driving, etc.
What would it even mean to say a specific individual has a 50% chance of getting into an accident in the next year?
What I'm used to in formal probability is the idea that a probability represents expectations for the outcome if an event is repeated an infinite number of times (and if it's repeated an arbitrarily large number of times the outcomes will approach the true probability).
The probability of flipping heads on a balanced coin is 50%, meaning if you keep flipping coins for close to forever, eventually your number of heads will approach 50% of your total flips.
But our individual driver does not repeat the next next year of their life an infinite number of times, so this kind of model doesn't apply.
If 50% of new drivers get in an accident in their first year, we can say that if you had a list of all new driver's a picked drivers at random, guessing that they would have an accident in the next year, you would be right 50% of the time (as your number of guesses approached infinite). But that's tautological.
I find the improper translation of statistics into probabilities especially common around the idea of risk. If a statistic says that your risk of an accident increases by 10% for every 5mph above 60 you're driving, that doesn't mean that you're rolling the dice by driving 70. The existence of the statistic will not manifest an accident out of nothing. There have to be casual forces at play.