4 ms·

It's not quite a single sentence, but IMO the best example of the prosecutors fallacy is the lottery: The chance of winning the powerball lottery is 300 million

by DSMan195276 3y ago

It's not quite a single sentence, but IMO the best example of the prosecutors fallacy is the lottery: The chance of winning the powerball lottery is 300 million to 1, so clearly anybody who wins _must_ have cheated since 300 million to 1 is practically impossible. Obviously that's not true, people legitimately win the powerball all the time despite the odds. The issue with this logic is judging the odds from the position of a _particular_ person winning vs. the odds of _anybody_ winning. Your individual odds are 1 in 300 million, but since the powerball gets many 100s of millions of entries clearly it's likely that eventually someone will win. Effectively, the prosecutors fallacy is presenting a very low probability as though that indicates something couldn't have happened. A probability alone is useless without the size of the population that probability is picking from, "low probability" events like winning the lottery happen all the time when your population is large enough.

joe_the_user 3y ago
That's a good explanation. The other to add is that someone combs a data file for "unlikely events" and finds one event they consider unlikely happened to a given person, you have to consider the probability of any event that looks unlikely occurring at all, not just the probability of that unlikely event happening.
eep_social 3y ago
Great explanation. I occasionally get to remind coworkers that at 100 requests per second, one in a million is about 8 times per day [1]. Usually mentioned in the context of handling, understanding, or planning for corner cases. [1] 100rps*60*60*24/1E6=8.64
cbsmith 3y ago
I often take it to the ridiculous point and use a scenario with only one possible positive case. Like: There is only one person in the world who is you. Let's say I had a facial recognition system that had a false positive rate of only 1 in a million. If I tried to find you by having the system scan through pictures of literally everyone on earth, how many people would I incorrectly identify as you?

joe_the_user 3y ago

That's a good explanation. The other to add is that someone combs a data file for "unlikely events" and finds one event they consider unlikely happened to a given person, you have to consider the probability of any event that looks unlikely occurring at all, not just the probability of that unlikely event happening.

eep_social 3y ago

Great explanation. I occasionally get to remind coworkers that at 100 requests per second, one in a million is about 8 times per day [1]. Usually mentioned in the context of handling, understanding, or planning for corner cases. [1] 100rps*60*60*24/1E6=8.64

cbsmith 3y ago

I often take it to the ridiculous point and use a scenario with only one possible positive case. Like: There is only one person in the world who is you. Let's say I had a facial recognition system that had a false positive rate of only 1 in a million. If I tried to find you by having the system scan through pictures of literally everyone on earth, how many people would I incorrectly identify as you?