The Simple Question That Stumped Everyone

It's quite fitting that Marilyn vos Savant's
last name in French means "learned"
Learning came easy to her considering she
had an IQof 228!
Vos Savant was born in St Louis, Missouri
on August 11, 1946 to immigrants from
Germany and Italy.
Her parents never told her she was
exceptional.
She once said in an interview: "No one
really paid much attention to me, actually.
As I said, mostly because I was a girl and I
accepted that."
But the world would pay attention in
1985 when she topped the Guinness Book
of World
Records list as the smartest person in the
world.
She was nearly 40 when she shot into the
spotlight.
Parade Magazine wrote a profile on her,
and readers had so many questions for
her that
the magazine offered her a Sunday
column, "Ask Marilyn" - which exists to
this day.
In this column, she ignited one of the
fiercest debates in probability of the 21st
century!
In 1990, a reader asked her the following
question:
Suppose you're on a game show, and
you're given the choice of three doors.
Behind one door is a car, behind the
others, goats.
You picka door, say #1, and the host, who
knows what's behind the doors, opens
another
door, say # 3, which has a goat.
He says to you, "Do you want to pick door
#2?"
Is it to your advantage to switch your
choice of doors?
This is known as the Monty Hall problem,
named after the former host of the game
show Let's
Make a Deal.
Is it behind door number 1, door number
2, or door number 3?
So, would it be in your interest to switch
from door number 1 to door number 2?
'll give you a few seconds to think about
it.
Most people assume that both doors are
equally likely to have the prize.
So they don't see the benefit of switching.
However, Vos Savant replied: "Yes; you
should switch.
The first door has a 1/ 3 chance of winning,
but the second door has a 2/ 3 chance."
She got so much heat for this response
and couldn't have imagined the backlash
that
would follow.
She received thousands of angry letters
and said 90% of them told her she was
wrong.
Scott Smith who has a PhD from the
University of Florida wrote: There is
enough mathematical
illiteracy in this country, and we don't
need the world's highest IQ propagating
more.
Shame!
Here's a letter from Professor Robert
Sachs of George Mason University:
You blew it!
As a professional mathematician, I'm very
concerned with the general public's lack
of mathematical skills.
Please help by confessing your error and
in the future being more careful."
Don Edwards of Oregon put it this way:
Maybe women look at math problems
differently than
men.
But actually, these people who sent her
some not-so- nice letters were utterly
wrong.
Switching your door DOES increase your
probability of winning.
When you first choose door #1, there's a
1/ 3 chance that the prize is behind that
one.
The two other doors together have a 2/ 3
chance of winning.
Then the host helps you out by opening up
the door they KNOW is a loser.
This improves your odds that the prize is
behind door 2.
Because door 2 must have the rest of the
chances.
It went from having a 1 in 3 chance to a 2
in 3 shot at the prize since the host
filtered
out the bad door, door number 3 for you.
Or put another way:
Switching doubles your odds of winning.
So yah I'Il choose door number 2 and
thank you for the extra 33. 3%.
The outcry against vos Savant was so
extreme that she felt compelled to devote
several
other columns to explaining her logic.
She noted that the benefits of switching
can be proven if you were to play through
the
six games that exhaust all possibilities.
This is contingent on the host always
opening a door with a goat.
Mapping out all the possibilities shows
there's a higher chance of winning if you
switch than
if you stay.
It's easier to understand the problem if
there are many more doors.
Say you chose 1 door out of 100.
The host then eliminates 98 doors that
they know don't have a prize behind them.
That leaves two doors - the one you chose
and the only other one remaining.
Do you switch now?
Absolutely.
When you first picked, you only had a
1/ 100 chance of getting the right door.
The odds of it being behind the other
doors was 99/ 100.
The host then filters out the options for
you by eliminating 98 bad doors that they
know don't have the prize.
This is tO your advantage because it leaves
the remaining door with the rest of the
odds,
a 99/ 100 chance of having the car.
Some eventually admitted they were in
the wrong.
A team at the Massachusetts Institute of
Technology worked on the problem, and
afterward, Seth
Kalson of MIT admitted:
You are indeed correct.
"My colleagues at work had a ball with
this problem, and I dare say that most of
them,
including me at first, thought you were
wrong!"
To which she responded:"Thanks, M.I.T.
needed that!"
And that math professor I mentioned
earlier who sent that not so friendly
letter?
Professor Sachs later conceded, writing:
"After removing my foot from my mouth
I'm now eating
humble pie.
I vowed as penance to answer all the
people who wrote to castigate me.
It's been an intense professional
embarrassment."
Our biggest misconception is assuming
that two choices mean a 50-50 chance of
something
happening.
This makes sense if we don't have any
other information.
If I picked two people and asked who
would win a tennis match and you don't
know anything
about them, you have a 50-50 shot of
getting it right.
But if I said Player Ajust took up the sport
yesterday while Player B has won
Wimbledon,
this would likely change your choice.
Information matters.
Just like when the game show host KNEW
which door had a goat.
They weren't opening up a door randomly.
The general idea is the more you know,
the more informed decisions you can
make.
Vos Savant once said: "People that we
think are very smart are not necessarily
very smart."
She explained they're more likely to be
educated or experienced rather than
intelligent.
What does she think is holding people
back from their intellectual potential?
She's been critical of compulsory
schooling because she says students learn
passively;
they sit there and are told what to believe
instead of learning to think independently.
She went so far as to say: "I would rather
not see compulsory schooling."
As for herself, she never graduated from
university, dropping out of Washington
University in St.
Louis after two years to start a career in
investment before following her real
passion,
writing which led to her famous answer to
the problem that stumped the world.
There's another way to learn that doesn't
involve sitting in a classroom.
Brilliant is an online interactive learning
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