[Reading level: C1 – Advanced]
In 1990, a small probability problem published in the American magazine Parade sparked one of the most famous controversies in the history of probability theory. It not only confused ordinary readers, but also led many professors, Ph.D. holders, and mathematicians to confidently insist on an answer that was… wrong.
At the center of the story was Marilyn vos Savant, who was once recognized by Guinness World Records for having an exceptionally high IQ. She wrote the “Ask Marilyn” column in Parade magazine, where readers sent in difficult questions about logic, mathematics, and life.
In September 1990, a reader named Craig F. Whitaker sent Marilyn a probability question based on the American television game show Let’s Make a Deal, hosted by Monty Hall. The problem later became known as the Monty Hall problem. The situation was exactly like the transcript you provided: a contestant stands in front of three doors; behind one door is a car, while behind the other two are goats. The contestant chooses one door. Then the host, who knows where the car is, opens one of the remaining doors to reveal a goat and asks whether the contestant would like to switch to the final unopened door.
Using ordinary intuition, many people believed that only two doors remained, so the probability must now be 50–50. Switching or staying seemed to make no difference.
But Marilyn gave a very short and confident answer: switch doors.
According to her, if the contestant kept the original choice, the probability of winning was only 1/3. If the contestant switched to the remaining door, the probability of winning would become 2/3.
This was exactly the point that caused an explosion of controversy across America. According to various later accounts, after the answer was published, the magazine received around 10,000 letters of protest, including nearly 1,000 from people holding Ph.D. degrees. Many of the letters were written on official letterhead from mathematics departments, statistics departments, or universities.
What made the story remarkable was not simply that Marilyn was correct, but the way so many highly educated people criticized her in an extremely harsh tone.
One of the most famous letters came from Robert Sachs, Ph.D., of George Mason University. He essentially wrote that Marilyn was completely wrong. In the English version quoted in many places, he said: “You blew it!” In other words, “You completely messed this up!” He argued that once a losing door had been opened, the remaining two choices became equal, each with a probability of 1/2. As a professional mathematician, he also expressed concern about the public’s lack of mathematical understanding and demanded that Marilyn “confess your error” publicly and be more careful in the future.
Another criticism came from Scott Smith, Ph.D., of the University of Florida. Writing in a sarcastic tone, he said that America already had enough “mathematical illiteracy,” and did not need the person with the world’s highest IQ spreading more misinformation. He ended his letter with a single word: “Shame!”
Another scholar, Kent Ford from Dickinson State University, reacted strongly as well. He essentially said he was shocked that Marilyn still could not recognize her mistake after at least three mathematicians had already corrected her. Some critics even mocked her by suggesting that perhaps she should keep the addresses of a few high school or college students so they could help her with future columns.
These criticisms did not merely reject her answer. They often sounded dismissive and condescending, as if Marilyn did not understand even basic probability theory. Ironically, the people attempting to “teach” Marilyn were the ones making the mistake.
The key issue lay in one tiny but extremely important detail: the host does not open a door randomly. He knows exactly where the car is and always opens a door hiding a goat. Therefore, his action does not reset the probabilities equally.
At the beginning, when the contestant chooses one door, the probability of picking the car is only 1/3. That means the probability that the car is behind one of the other two doors is 2/3. When the host opens one of those two doors and reveals a goat, he does not eliminate the original 2/3 probability. He merely removes one incorrect option from that group. As a result, the entire 2/3 probability effectively transfers to the one unopened door that remains.
An easier way to understand this is the 100-door example mentioned in your transcript. Imagine there are 100 doors. You choose one door, meaning your chance of being correct is only 1%. The host then opens 98 goat doors, leaving only your chosen door and one other unopened door. In that situation, almost everyone immediately feels that switching is the better choice, because the original choice was almost certainly wrong. The logic behind the three-door version is exactly the same; it simply feels more deceptive because the numbers are smaller.
Despite the wave of criticism, Marilyn did not withdraw her answer. Instead, she continued using later columns to explain the problem in different ways: simulations, probability tables, and examples with larger numbers of doors. Eventually, mathematical calculations and computer simulations consistently produced the same result: contestants who always switched won about 2/3 of the time, while those who always stayed with their original choice won only about 1/3 of the time.
An especially interesting detail is that even Paul Erdős, one of the most famous and influential mathematicians of the 20th century, initially refused to believe the “switch doors” solution. According to later accounts, he was only convinced after seeing computer simulations repeatedly demonstrate that switching won significantly more often.
Eventually, many of Marilyn’s critics admitted they had been wrong. Among them was Robert Sachs — the same man who had demanded that Marilyn publicly admit her mistake. He was later reported to have written an apology letter after realizing he had been wrong himself. He acknowledged that his excessive confidence had misled him and viewed the incident as a painful lesson about intellectual arrogance.
The Monty Hall story therefore became more than just a probability puzzle. It became a lesson about the way human beings think. Sometimes, an argument that feels “obviously true” can still be wrong. And sometimes, advanced degrees do not protect people from faulty intuition.
Marilyn vos Savant stood in the middle of an intense storm of criticism, where many people attacked her not only with logic, but also with ridicule. Yet in the end, mathematics was on her side.
Perhaps the greatest lesson of the story is not “always switch doors,” but this: when facing a problem that goes against intuition, the greatest danger is not ignorance — it is being absolutely certain that you are right.
WORD BANK:
probability /ˌprɑː.bəˈbɪl.ə.t̬i/ [B2] (n): xác suất
spark sth /spɑːrk/ [C1] (v): châm ngòi, gây ra
controversy /ˈkɑːn.trəˌvɝː.si/ [C1] (n): cuộc tranh cãi
ordinary /ˈɔːr.dən.er.i/ [B1] (adj): bình thường
insist on sth /ɪnˈsɪst ɑːn/ [B2] (v): khăng khăng, nhất quyết về cái gì
column /ˈkɑː.ləm/ [B2] (n): chuyên mục (báo)
send in sth /send ɪn/ [B2] (v): gửi (bài, đơn…)
contestant /kənˈtes.tənt/ [B2] (n): thí sinh
host /hoʊst/ [B1] (n): người dẫn chương trình
reveal sth /rɪˈviːl/ [B2] (v): tiết lộ
intuition /ˌɪn.tuˈɪʃ.ən/ [C2] (n): trực giác
account /əˈkaʊnt/ [B2] (n): bản tường thuật, tài liệu tổng hợp
protest /ˈproʊ.test/ [B2] (n): sự phản đối
letterhead /ˈlet̬.ɚ.hed/ (n): tiêu đề thư, tiêu đề bài viết
statistics /stəˈtɪs.tɪks/ [B2] (n): số liệu thống kê
in a(n) + adj + tone /ɪn ə … toʊn/ (phr): với giọng điệu…
quote /kwoʊt/ [B2] (v): trích dẫn
blow it /bloʊ ɪt/ (idiom): làm hỏng việc
mess sth up /mes … ʌp/ [B2] (v): làm hỏng cái gì
confess sth /kənˈfes/ [B2] (v): thú nhận, thừa nhận
error /ˈer.ɚ/ [B2] (n): lỗi, sai sót
sarcastic /sɑːrˈkæs.tɪk/ [C1] (adj): mỉa mai
illiteracy /ɪˈlɪt̬.ɚ.ə.si/ [C2] (n): nạn mù chữ
mock sth /mɑːk/ [C1] (v): chế giễu
dismissive /dɪsˈmɪs.ɪv/ [C1] (adj): coi thường, bác bỏ
condescend /ˌkɑːn.dɪˈsend/ [C2] (v): tỏ vẻ bề trên
ironically /aɪˈrɑː.nɪ.kli/ [C1] (adv): trớ trêu thay
randomly /ˈræn.dəm.li/ [B2] (adv): một cách ngẫu nhiên
reset sth /ˌriːˈset/ [B2] (v): đặt lại
eliminate /ɪˈlɪm.ə.neɪt/ [B2] (v): loại bỏ
transfer to sth /trænsˈfɝː tə/ [B2] (v): chuyển sang cái gì
deceptive /dɪˈsep.tɪv/ [C1] (adj): gây hiểu lầm, đánh lừa
withdraw sth /wɪðˈdrɔː/ [B2] (v): rút lại, thu hồi
simulation /ˌsɪm.jəˈleɪ.ʃən/ [C1] (n): sự mô phỏng
influential /ˌɪn.fluˈen.ʃəl/ [C1] (adj): có ảnh hưởng
initially /ɪˈnɪʃ.ə.li/ [B2] (adv): ban đầu
solution /səˈluː.ʃən/ [B1] (n): đáp án
demonstrate /ˈdem.ən.streɪt/ [B2] (v): chứng minh
eventually /ɪˈven.tʃu.ə.li/ [B2] (adv): cuối cùng
critic /ˈkrɪt̬.ɪk/ [B2] (n): nhà phê bình
acknowledge /əkˈnɑː.lɪdʒ/ [B2] (v): thừa nhận
excessive /ɪkˈses.ɪv/ [C1] (adj): quá mức
incident /ˈɪn.sə.dənt/ [B2] (n): sự việc, vụ việc
arrogance /ˈer.ə.ɡəns/ [C1] (n): sự kiêu ngạo
puzzle /ˈpʌz.əl/ [B2] (v): làm bối rối
faulty /ˈfɑːl.t̬i/ [C1] (adj): có lỗi, sai sót
intense /ɪnˈtens/ [B2] (adj): dữ dội, mãnh liệt
a storm of criticism /ə stɔːrm əv ˈkrɪt̬.ə.sɪ.zəm/ (n): làn sóng chỉ trích dữ dội
ridicule /ˈrɪd.ə.kjuːl/ [C1] (n): sự chế giễu
go against sth /ɡoʊ əˈɡenst/ [B2] (v): đi ngược lại cái gì
ignorance /ˈɪɡ.nɚ.əns/ [C1] (n): sự thiếu hiểu biết
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