I hate math, but there’s this statistics problem that has me geeking out. It’s a
question that seems really really simple but it’s stumped me. And not just me, it has
stumped thousands of people around the world including math professors and leading statisticians.But
before we dive in I’m going to introduce you to Zachery Crockett. He first introduced
me to the puzzle and I called him up to talk about it.
My name is Zachery Crockett, I’m a writer for Priceonomics.
Zachery and his girlfriend were confused by the problem too.
We just sat there debating the answer to this problem for two hours and I don’t think
any of us really understood it. The puzzle we were all stumped by is called
the Monty Hall Problem -- named after the host of the game show that made it famous.
the problem goes like this: there’s a brand new car behind one of three doors. Behind
the other 2 are goats. Say you pick door 1. Monty then shows you the goat behind one of
the doors you DIDN’T choose - say, door 3. Now here’s the question: You’re allowed
to change your answer to Door 2. Do you switch? Or stick with your original choice?
So yeah, I got interested in the Monty Hall Problem, did a little research, and then I
found out there was this whole second angle to the story.
You’ve never met a man that feared you a little bit because he thought you were much
brighter than he was? That’s Marilyn Vos Savant in 1988 being
interviewed by Joe Franklyn. Yeah maybe I’ve met a man or two, maybe
a couple a hundred like that. Marilyn is very intelligent. In fact:Back
when the Guinness World Records actually kept track of this she was the world’s highest
IQ. She now writes for Parade Magazine and has
for the last 20 years. So the premise of the column was of course,
like, here is the person with the world's highest IQ here to answer your challenging
math questions. This brings us to September 1990, when a reader
submitted to Marilyn... the Monty Hall Problem. Is it to your advantage to switch your choice
of doors? Now, if you’re like me the obvious answer
is no. There’s no advantage of switching doors at all, There are two doors so the chance
of getting a car and not a goat is 50/50. Bing. Bang. Boom.
But that’s the wrong answer, and Marilyn knew that.
She replied: “Yes; you should switch.” And here’s why.
Here are 3 doors. There’s a goat behind 2 and a car behind
1. In a blind test, you’re more likely to pick
a goat than a car. In fact, you’re 2/3RDS likely so let’s use that as our main scenario.
You pick door 1. So now, Monty Hall, who knows what’s behind
all the doors, is forced to reveal a goat regardless of the door you pick. Since, in
the most probable scenario you’ve also picked a goat, the only door left is the one with
the car. So, now Monty Hall asks, “Would you rather
keep the door you’ve picked, or switch?” Well, you should most definitely switch. If
you do you get the car 2/3rds of the time. Turns out when Marilyn correctly answered
the Monty Hall Problem, she received thousands of letters from across the world telling her
she was flat out wrong. I think part of her was a little bit surprised
that she received 10,000 letters calling her an idiot. There was, without a doubt a little
bit of sexism at play here. Not only was her answer right, it wasn’t anything new.
The first time the Monty Hall problem was published was in 1975. This guy named Steve
Selvin at Berkeley presented the problem in The American Statistician.
Selvin said you should switch and no one argued with him. And over the next 15 years multiple
other academics reiterated the same problem without and no one ever told them that they
were wrong. Then in 1990 Marilyn answered the same question
correctly and people went bananas. Marilyn ended up and tallying up what percentage
of the 10,000 responses claimed she was wrong. Only 8% of readers actually agreed with her
and after subsequent columns she was able to raise that to 56%. And among academics:
It was 35% among academics initially supporting the answer. And about 70% of academics ultimately
decided to agree with her. The only way she managed to get people on
her side was by asking them to do the experiment themselves. Elementary, middle school, and
high school teachers from all over the country wrote in, astounded that their students were
able to prove her right.It’s easy now to do a simple google search of this little sucker
of a problem and get a million explanations on how to arrive at the right answer.
There's something about this problem that really strikes a chord with, not only statisticians,
but just everyday problem solvers and people.