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So imagine you’ve again succeeded to sneak in a party where you were not invited, and
you’re discussing with people you’ve never met before.
At some point, you hear the story of Linda, 31 years old, single, outspoken, and very
bright. You learn that Linda majored in philosophy, and as a
student, she was deeply concerned with issues of discrimination and social justice, and
participated in anti-nuclear demonstrations.
Two people are arguing about a detail though: one of them thinks that Linda has now become
a bank teller , but the other says that besides being a bank teller, she is also active in
the feminist movement. What would YOU find more probable, that Linda is a bank teller,
or that she’s a bank teller AND active in the feminist movement?
You’ve probably answered the second option, as do 90% of people asked! But surprisingly,
it turns out that this is not the (mathematically) correct answer.
To understand why, imagine that this circle represents people who are bank tellers in
the world. This other circle represents people who are active in the feminist movement. Actually,
the two circles should overlap : some people will indeed be both bank tellers and active
in the feminist movement.
Now visually, it is very clear that this area in the middle is smaller than this whole blue
area. What that means is that the number of feminist bank tellers will always be smaller
than the number of bank tellers in general, that includes feminist bank tellers, but also
all sorts of bank tellers with interests in other domains! Your math teacher would say
that “the probability of two events occurring together is always less than or equal to the
probability of either one occurring alone.”
This is why it’s incorrect to assume it’s more probable that Linda is a bank teller
AND active in the feminist movement.
It is disputed what to conclude from this experiment: are people bad at maths? Is it
really a reasoning mistake ? Or is it just that the word “probable” can mean multiple
things, the mathematical concept and a less stric meaning of “plausible”? It’s indeed
the case that in real-life situations, it’s often useful to assume that what your interlocutor
says is relevant somehow, so if you learn details about Linda before you’re asked
a question, you can reasonably assume that those details must be relevant to answer the
question. No matter how you interpret this experiment, the fact is that this bias exists
and could play tricks on you in real-life situations if you’re not careful!
And in case you still don’t believe us on what is the correct answer, try to consider
now that 100 persons fit the above description of Linda. Would there be more people bank
tellers or more people active in the feminist movement and bank tellers? Now the effect
should disappear and you should intuitively get the correct answer!
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