PSA
Some notation first:
P(Z) = Probability of Z being True
P(Z|Y) = Probability of Z being true given Y is true
P(A and B) = Probability A and B are both True
Now the message; You Probably Misunderstand Probability & Statistics
Example:
“1 in 3 people has X” doesn’t mean that if you’re a group of 3, one of you surely has X.
P(At least one of you has X) = 1 - P(none of you has X) = 1 - (2/3)^3 = 0.7
P(Exactly one of you has X) = (1/3)*(2/3)^2 = 0.15
What “1 in 3 people has X” means, is that the bigger a group of people is, the more probable it is that the percentage of them which has X is closer & closer to 1/3.
If you have a group of 1 million people, it’s likely that the amount of people which have X is somewhere around 333,000.
Another one:
This one’s a REAL goodie, we see it pop up in politics all the time.
P(A|B) isn’t the same as P(B|A).
Take, for example, the statements we all know from current politics of “almost all terrorists are Muslim fanatics”, and “therefore most Muslims are probably fanatic terrorists”.
Now the latter statement is obviously not true, and with the huge amounts of terrorism motivated by white supremacy, we know even the former statement is not true.
But let’s assume the latter statement WAS true, and most acts of terrorism were made by Muslim fanatics, and see what we get regarding Muslim people in general.
The logical error we see so much in politics about Muslim people is:
“P([X is a fanatic terrorist] | [X is Muslim]) =
P([X is Muslim] | [X is a fanatic terrorist])”
That statement is just not true from a mathematical standpoint.
I INTRODUCE YOU TO: BAYES’ FORMULA
P(A|B)*P(B) = P(A and B) = P(B|A)*P(A)
In our case with Muslim people and terrorism, we get:
P([X is a fanatic terrorist] | [X is Muslim]) =
P([X is Muslim] | [X is a fanatic terrorist])*P(X, a randomly selected person from all the people on Earth, is a terrorist)/P(X, a randomly selected person from all the people on Earth, is Muslim)
Now let’s look at the ratio:
P(X, a randomly selected person from all the people on Earth, is a terrorist)/P(X, a randomly selected person from all the people on Earth, is Muslim)
What is the probability that a randomly selected person from all of Earth is Muslim?
Roughly 1 in 7.
There are a LOT of Muslim people in the world.
And what is the probability of a randomly selected person from everyone on Earth to be a terrorist?
Practically zero, I hope we can agree on that.
Therefore, even if all terrorists were Muslim fanatics, which they aren’t, we would STILL get:
P([X is a fanatic terrorist] | [X is Muslim]) =
= 1*[practically zero]/(1/7) =
practically zero
