So, they say it's very unlikely

that Linda now works for bank based on the description.

And the last option, "Linda is a bank teller who's active

in the feminist movement" usually gets sort of an average rank.

Now, let's think about whether this is really possible.

Before we think about Linda,

allow me to go back in an abstract fashion to two events.

A and B.

And here we have what's called a van diagram.

There's a sample space S- or the possible outcomes

there's a set on event A of some outcomes

B of some other outcomes

and A and B may have an intersection.

We saw an example of this sort in a previous lecture.

Now notice, the intersection of A and B

remember from middle school Math, those are the elements

that are both in A and in B.

This set A intersected B

is smaller than A and is also smaller than B.

It builds a subset of A

and it builds a subset of B.

What this means is that it has at most as many

usually fewer elements in it than A and B.

And therefore the probability of the intersection

must be smaller or equal than the probability

of the individual events.

P of A and P of B.

Let me illustrate this again with a simple example of a Fair Die.

Look at this picture here.

A Fair Die has 6 possible outcomes.

1, 2, 3, 4, 5, 6.

A are the even numbers.

2, 4, 6.

B are the first four numbers.

1, 2, 3, 4.

The 5 is neither an A and B, but it's an S, so that's outside

the two circles representing the events

but it's still within S.

Notice now the intersection.

The elements that are both in A and in B

those are the two numbers 2 and 4.

And here look at this, the intersection probability of A in the sector B

is 2 out of 6 that's smaller equals 3 and 6 of A,

and it's also small equal 4 and 6 of B.

This is a general rule.

So, if this is a general rule,

your subjective probabilities must obey this rule.

Now let's return to Linda.

Look at C, F and H.

"C" is "Linda's active in the feminist movement".

"F" is "Linda is a bank teller".

"H" says "Linda is a bank teller who is active in the feminist movement".

Ah! Look at H!

That's C and F simultaneously!

That's intersection.

What this means is that Linda is a bank teller who's active

in the feminist movement.

Must be ranked below bank teller

And must be ranked below feminist movement.

Of course, your personal opinion may be it's very likely

that Linda is a bank teller, maybe she thought it out

and she wanted to make a lot of money in later life?

You can rank bank taller ahead of feminist.

But no matter what you think the intersection probability

is gonna be smaller or equal.

So, whatever your favorite ranking is

H must rank below F and it also must rank below C.

So, subjective probability must satisfy these 2 inequalities.

I can tell you

I have give out hundreds and hundreds of times this questionnaire

usually more than 80% of the students in a class

get this wrong.

So if you picked the wrong option before

you're in good and large company.

This actually is an example of the famous fallacy

a famous way how we, humans, think incorrectly

it's called a conjunction fallacy.

It was first documented in a series of experiments

done by 2 famous psychologists Amos Tversky and Daniel Kahneman.

And here I give you citation of a famous paper in psychology

from 1983.

Sadly, Amos Tversky died of cancer

before he could have gotten the Nobel Prize

so Daniel Kahneman got the Nobel Prize in economics

for his work, not on this fallacy and other fallacies as well

sometime later.

This work is extremely influential in areas such as behavioral economics

and behavioral finance.

You may have heard about these fields that are now very popular

not only in academia, also in industry

and I encourage you to google these terms: conjunction fallacy,

behavioral economics, behavioral finance to learn more

about these fallacies, these mistakes that we make in decision making.

To wrap up.

Two events occurring simultaneously cannot be more likely

than the individual events by themselves.

But often, in our judgement course we make that error

it has been well documented in many experiments

it's called the conjunction fallacy.

So, be careful with your subjective probability.

Ir cannot be true that anything is possible.

Obviously, the probabilities are between 0 and 1.

Not 120%, not -5%.

But in addition, there's also this intersection rule

to conjunction fallacy, so be careful when you develop

your gut feeling into subjective probabilities.

Once again, thanks for your attention.

I see you in the next lecture.