No I don’t think that’s it. I would express it this way.
The chance of me reading a haircut meme straight after getting a haircut is near zero. But there are multiple people reading the haircut meme. So if you post a haircut meme, there is a high chance that ANY ONE of the readers will be straight after getting a haircut.
Like Sally Clark was convicted because the chance of having two miscarriages in a row is a million to one - it’s not plausible. The only other explanation is that she murdered her babies, so that’s the only plausable explanation.
But in a population of 60 million people, you are likely to find someone (or 60 people) who have had two miscarriages in a row. She was just the unlucky one.
Wikipedia has more detail and intersting angles, like the defendent’s fallacy, why it is a fallacy and when it might be correct.
Then there’s more stuff, and what happened after the conviction… That pathologist was never even charged with a crime, or lynched.
edit:
But your point is interesting too. The chance of winning the lottery given that I’ve just had a coffee is very low. But the chance that I’ve just had a coffee given that I’ve won the lottery is very high. But if I drink a coffee and then immediately win the lottery, people might assume that having just had a coffee improves my lottery chances.
I don’t know if there is a name for that one, but it sounds like something people do a lot.
I get sick, take medicine, get better. Then chance of having taken medicine given that I get better is 100%. So people will assume the medicine helps. But the chance that I get better given that I’ve taken medicine might be 10%. The chance I get better if I had not taken medicine might be more than 10%, but that result is not obvious at all.
Ah your explanation clears it up. That whole conditional probability thing is in the wikipedia article, but I see now that my explanation of the haircut thing was not correct.
I guess maybe this is a better formulation:
p1 = P(not being guilty | evidence found)
vs
p2 = P(evidence found)
Prosecutor’s fallacy would assert that, if p2 is small say 0.01%, then the defendent is guilty. But really the relevant probability is p1, which could be quite a bit larger than 0.01%.
No I don’t think that’s it. I would express it this way.
Like Sally Clark was convicted because the chance of having two miscarriages in a row is a million to one - it’s not plausible. The only other explanation is that she murdered her babies, so that’s the only plausable explanation.
But in a population of 60 million people, you are likely to find someone (or 60 people) who have had two miscarriages in a row. She was just the unlucky one.
Wikipedia has more detail and intersting angles, like the defendent’s fallacy, why it is a fallacy and when it might be correct.
Then there’s more stuff, and what happened after the conviction… That pathologist was never even charged with a crime, or lynched.
edit:
But your point is interesting too. The chance of winning the lottery given that I’ve just had a coffee is very low. But the chance that I’ve just had a coffee given that I’ve won the lottery is very high. But if I drink a coffee and then immediately win the lottery, people might assume that having just had a coffee improves my lottery chances.
I don’t know if there is a name for that one, but it sounds like something people do a lot.
I get sick, take medicine, get better. Then chance of having taken medicine given that I get better is 100%. So people will assume the medicine helps. But the chance that I get better given that I’ve taken medicine might be 10%. The chance I get better if I had not taken medicine might be more than 10%, but that result is not obvious at all.
Ah your explanation clears it up. That whole conditional probability thing is in the wikipedia article, but I see now that my explanation of the haircut thing was not correct.
I guess maybe this is a better formulation:
p1 = P(not being guilty | evidence found)
vs
p2 = P(evidence found)
Prosecutor’s fallacy would assert that, if p2 is small say 0.01%, then the defendent is guilty. But really the relevant probability is p1, which could be quite a bit larger than 0.01%.
Anyways let me know if you agree lol.