Someone says “you have 1 out of 370 chances to win a bottle of water”
and you win 2 consecutive times in a row, what does that mean? i’m lucky or the probability is wrong?
In: Mathematics
You can’t tell if a probability is wrong from a single trial.
If something claims to have a 1/370 of happening, and you did it 370 times and you won every single time, then that probability is probably bullshit.
If you tried it twice, that’s not enough to determine anything.
There’s a lot of fairly complicated statistics you can do to work out how likely it is that you would see the results you’ve seen, assuming a certain probability. E.g, given that the chance of winning is genuinely 1/370, what are the chances that the first 2 results would be a win? And you’d probably discover that it’s unlikely, but not impossible, so you don’t have enough evidence to say that the estimate of the probability is wrong.
I would love to give a quick and simple explanation for how you do that, but there isn’t one, it’s complicated maths and any attempt to simplify it would be dishonest.
But, the important thing is: you can’t intuit it. Human brains are bad at interpreting probability. You can’t flip a coin a bunch of times and determine whether it’s fair by judging how fair it _feels_, what you do is write the results down and check if it actually is fair. I remember playing a dice-based video game, and I was confident that the dice were unfair and I was getting more low numbers than I should have. So, because I’m a nerd, I got out a pen and paper, and started noting the results… and it turned out I was wrong, the results were entirely fair, and I was noticing a pattern that didn’t exist.
It happens all the time, just try playing a board game with a superstitious person.
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