Well, that really depends on what probability you’re asking about. Perhaps it is more clear to say: The statistics of past events do not determine the probability of future events.
(At least not in and of themselves.)
An obvious example: Suppose you flip a coin three times. Your statistics, especially with the sample set being so low (and odd for that matter), naturally won’t reflect the intuitive 50/50 probability of flipping heads the fourth time.
What if you flip a coin 10 times and get heads each time? Does flipping 10 heads in a row imply anything at all about probability of flipping heads on your eleventh flip? (The answer is no.)
I bring this up because it’s annoyingly astounding how many times people will bring up statistics as evidence of societal privilege, oppression, or institutional racism / sexism.
For example, one may find that at a certain company, only 5% of the employees are black, and 95% are white. Does this mean a black person picked from the general population at random is far less likely than a white person to get a job there? Of course not. Firstly, that statistics of who’s already been hired doesn’t tell us anything about applicants who weren’t hired (are less black people applying in the first place?), and secondly, we’re ignoring quite a lot of other variables, such as interest in what the company does and necessary qualifications.
To make the fallacy a little more obvious: Suppose the company has 100 employees, 5 of which are black (thus 5%). Then a white person retires and they hire a black person in his place. Does this mean the probability of any random black person getting a job there just rose by 1%? That is, does hiring a black person increase the probability of any random black person being hired? Obviously not. (At least, I hope it’s obvious.)
And yet this fallacious way of interpreting statistics is brought up again and again in discussions of race and sex and privilege, as though the statistics of past events alone somehow determine the likelihood of your future. (“You have so many opportunities! Just look at the stats!”)
What’s even sadder is that this way of thinking seems persuade amiable people to believe that they have some kind of moral obligation to put themselves down based on their race or sex for the greater good, as in: “I shouldn’t apply for that job because I have white male privilege; that job should really go to a minority who doesn’t share my privilege!” or “I shouldn’t seek financial aid for my white children because they already have so many opportunities already just by virtue of being white!”
You don’t make the world better with that sort of thinking. You make it worse.