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.