Hi, so far in this course we've discussed 
a wide variety of inductive arguments. 
First of all, we looked at statistical 
generalization from a sample. 
Then we looked at application of the 
generalization down to a particular case. 
Then we looked at inference to the best 
explanation, and argument from analogy. 
And last week we turned to causal 
reasoning, which involved the positive 
necessary and sufficient condition test. 
And, in addition, at the very end, we 
looked at concommitent or concommitent 
theoriation, which involved a kind of 
manipulation in drawing conclusions about 
what causes what. 
So we've seen a lot of kinds of 
induction, 
and that's gotta raise the question, 
what's in common to all the different 
types of induction that makes them 
induction? 
What we saw, the inductive arguments, 
unlike deductive arguments, are 
defeasible, 
and they don't even aim at being valid. 
Instead, they just try to be strong. 
But strength comes in different degrees, 
and we haven't really learned anything 
yet about, what exactly strength is? 
Well, it turns out that one way of 
understanding inductive strength is that 
an argument is strong in proportion to 
the probability that its conclusion is 
true, given its premises. 
So inductive strength can be understood 
in terms of probability. 
And so for this week, we're going to turn 
to the notion of probability, which will 
help us understand inductive arguments. 
But, probability is important in a lot of 
other ways too. 
I mean just think about going on a picnic 
tomorrow. 
You want to know what the probability of 
it raining is, because if the probability 
of rain is very high, you might not want 
to go on your picnic. 
Instead, stay inside. 
Okay, so probability affects our beliefs, 
and it affects our decisions, and that 
makes it important to understand 
probability, and try to figure it out. 
But that's a problem, 
because if you just rest on your 
intuitions about probability, you're 
going to get messed up, you're going to 
make mistakes. 
Almost everybody messes up probability 
until they start thinking about it a 
little bit more seriously. 
Let me give you a few examples where 
people get confused about probability. 
[SOUND] Seven, alright. 
[SOUND] Seven, alright. 
[SOUND] Another seven. 
Unbelievable. 
Cool. 
Three sevens in a row, and seven's a 
winning number. 
So, that's great but, you know, the odds 
of getting four sevens in a row are 
really slim, 
so I bet the next one's not going to be a 
seven. 
Right? 
No. 
Just because the first three were a 
seven, doesn't tell you the next one's 
not going to be. 
Sure, it's unlikely to get four in a row, 
but once you got the first three, then 
the likelihood of getting the fourth 
seven is just the same as the likelihood 
of getting a seven on any roll 
whatsoever. 
Some people make that mistake. 
They think that just because they got 
three in a row, it's not going to come up 
that way again the fourth time. 
And other people make the opposite 
mistake. 
They say, hey the dice are hot tonight. 
I got three sevens in a row. 
The next one I'm going to get a seven 
too. 
I'm going to put all my money on seven. 
Don't do it. 
You'll lose your money, because even if 
the first three are sevens, dice don't 
get hot. 
The odds of getting a seven on the fourth 
one are exactly the same after you've 
gotten three sevens, and as if you didn't 
get three sevens. 
And both of these mistakes. 
Three sevens, so the next one's not 
going to be seven. 
Three sevens, so the next one's going to 
be seven. 
They're both mistakes, because the odds 
on the fourth roll are not affected by 
the odds on the first three rolls. 
And people who think otherwise, they're 
just going to get fooled by gamblers. 
It's not just in gambling, too. 
It's also in basketball. 
People think, oh he's hot. 
He's made a lot of shots in a row. 
He's hot. 
He's going to make the next one. 
And then they'll tell that player, you 
take the shot, because you're hot 
tonight. 
Well that's a little more controversial 
in basketball, 
but some statistics suggest that people 
don't really have hot hands in 
basketball. 
They just make the percentage that they 
make. 
And you're going to get strings, but that 
doesn't mean you're hot in any way. 
Like I said, that's controversial, but 
with dice, at least we know that dice do 
not get hot, and so don't waste your 
money making that mistake. 
That's called the gambler's fallacy, and 
don't do it. 
Okay, deck of cards, and here I am. 
I'm going to shuffle the cards, okay, 
there we go. 
There we go, I'm going to shuffle the 
cards again. 
We've got these cards all shuffled and 
now I'm going to deal out two hands, 
okay. 
Nine, a queen, 
an eight, a queen. 
A five, a queen. 
A jack, a queen. 
A four, an ace. 
Wow, look at those hands. 
That's amazing. 
You think they're about equally probable? 
What's the likelihood of that hand coming 
up? 
Most people would say, that's pretty 
slim. 
It's unlikely that you're going to get a 
hand with four queens and an Ace. 
What about this hand? 
That's the kind of hand I get all the 
time when I play poker. 
So most people are going to think that 
kind of hand is a lot more likely, but 
actually, 
they're equally probable. 
Getting exactly this hand and exactly 
that hand have the same probability. 
The reason people think this one is less 
likely than this one, is that you get 
kind of hand a lot in poker, namely, a 
hand that is junk, it's useless. 
You get a winning hand like this, not 
very often in poker. 
And so people think that this one is less 
likely than this one because this hand is 
more a representative of the type of hand 
that I get when I'm playing, and that 
most people get when they're playing. 
But that's what's called the 
representativeness heuristic. 
You think it's more probable because it's 
more representative of the kind of thing 
that you encounter and experience. 
Another famous example of the 
representativeness heuristic comes from 
kind of Kahneman and. 
Tversky. 
It's about Linda the Bank Teller. 
They tested a large number of subjects. 
What they did is simply describe Linda. 
Linda is 31 years old, single, outspoken, 
and very bright. 
As a student, she majored in philosophy. 
She was deeply concerned with issues of 
discrimination and social justice, 
and sh also participated in anti nuclear 
demonstrations. 
And yes there's subjects to rank the 
following statements with respect to 
probability. 
You know, which one is more probable than 
which of the others. 
Linda is a teacher in an elementary 
school. 
Linda works in a book store, and takes 
yoga classes. 
Linda is active in the feminist movement. 
Linda is a psychiatric social worker. 
Linda is a bank teller. 
Linda is an insurance sales person, 
and Linda is a bank teller and is active 
in the feminist movement. 
And when people ranked all of these, 
they tended to put Linda as a bank teller 
and is active in the feminist movement as 
more likely than Linda is a banker 
teller. 
That can't be. I mean, just think about 
it. 
It's got to be less likely that she's a 
bank teller and active in the feminist 
movement, and simply that she's a bank 
teller, because in every possible state 
of affairs where she's a bank teller and 
active in the feminist movement, she's 
also a bank teller. 
So there have to be some possibilities 
where she's a bank teller, but not active 
in the feminist movement. 
So it has to be more likely that she's a 
bank teller than that she's both a bank 
teller and also active in the feminist 
movement. 
And why do people make this mistake so 
often? 
It's largely because, when they trust 
their intuitions about probability, those 
intuitions are based on what they take to 
be representative. 
Someone with a background like Linda, who 
is deeply concerned with issues of 
discrimination and social justice, are 
likely to be active in the feminist 
movement, 
whereas bank tellers are not typically 
known for being active in the feminist 
movement. 
So it would be more typical for her to be 
both than for her to just be a bank 
teller. 
And so they based their probability 
judgment on the representativeness 
heuristic, 
and that's what leads to the common 
mistake. 
One final common mistake about 
probability is illustrated by what has 
come to be known as The Monty Hall 
problem or sometimes the three door 
problem. 
Here's the setup, which comes from an old 
TV show called Let's Make A Deal. 
There are three doors on the stage, lets 
call them door A, door B and door C. 
And behind one of the doors is a car, 
and if you get the right door, you get to 
keep the car. 
But behind the other two doors is a goat, 
and if you get those doors, you go home 
with a goat. 
Now, we're assuming that you'd rather 
have a car than a goat. 
You might be one of those weird peoples, 
but let's assume you want a car and not a 
goat. 
Imagine that you picked door A, and then 
the host, Monty Hall opens door C, and 
reveals behind door C a goat. 
Now you know that there's door A and door 
B left. 
One of them has a car, one of them has a 
goat. 
And Monty Hall turns to you and he offers 
you the chance to switch from door A, the 
one you picked, 
to door B. 
And the question is, should you switch? 
And this has actually caused a lot of 
controversy, 
because some people think you should 
switch, some people think you shouldn't 
switch. 
I'm not going to tell you, because that's 
going to be one of our exercises. 
And the point of this lecture is just to 
show you that you can't trust your 
intuitions. 
Because so many people will get it wrong 
in the Monty Hall case, in the 
representativeness heuristic, and so many 
people commit the gambler's fallacy that 
you need to take probability seriously, 
and in the next lecture we'll start 
looking at some definitions of what it 
is, and the lectures after that we'll 
look at rules for probability, because 
you need that kind of thing if you can't 
trust your intuitions.