In September 1990, Marilyn vos Savant, holder of the highest recorded IQ, ignited a fierce debate that continues to captivate both mathematicians and the general public. Her controversial take on the Monty Hall Problemâa probability puzzle based on the classic TV game show Letâs Make a Dealâchallenged conventional wisdom and sparked intense reactions from experts. Here's the breakdown of the Monty Hall Problem and why Marilynâs answer, though initially criticized, turned out to be right!
𧩠The Monty Hall Problem: The Puzzle That Stumped Many
The scenario:
Three doors: Behind one is a car, behind the others, goats.
The contestant chooses a door. The host, knowing where the car is, opens a door to reveal a goat.
The contestant is then given the option: stay with their choice or switch to the other unopened door.
đ Marilynâs Bold Answer: âAlways Switchâ
Marilyn vos Savantâs answer was simple and clear: Switch doors. Her reasoning? Switching increases the chance of winning from 1/3 to 2/3. But this answer was met with a storm of criticism!
đ€Ż The Backlash
Over 10,000 letters poured in, many from PhDs, claiming:
âYou completely misunderstood probability.â
âThis is the biggest blunder Iâve ever seen!â
âMaybe women donât understand math like men do.â
đ The Truth: Marilyn Was Right
Hereâs the math: 1ïžâŁ Initial Choice Probability:
The chance of picking the car is 1/3.
The chance of picking a goat is 2/3.
2ïžâŁ Hostâs Knowledge:
If the contestantâs initial pick is a goat (2/3 chance), the host reveals the other goat. Switching guarantees a win.
If the contestantâs initial pick is the car (1/3 chance), switching leads to a loss.
Conclusion: Switching results in a 2/3 chance of winning, while staying gives only a 1/3 chance.
đĄ Why Does It Feel Counterintuitive?
1ïžâŁ Misjudging Probabilities: Many assume that after the host reveals a goat, the remaining doors each have a 50/50 chance, ignoring the original 1/3 and 2/3 probabilities. 2ïžâŁ Reset Bias: People often see the second choice as a fresh start, when itâs actually part of the initial setup. 3ïžâŁ Deceptive Simplicity: The three-door setup makes it feel simpler than it is, masking the complexity of the underlying math.
â Proof and Validation
Marilyn's answer was later confirmed by:
MIT running thousands of simulations, showing a 2/3 win rate for switching.
MythBusters testing the problem and verifying her explanation.
Apologies from academics who initially criticized her, admitting their mistake.
đ§ Marilyn vos Savant: A Genius Ahead of Her Time
IQ: 228, recognized by Guinness World Records.
By age 10, she read all 24 volumes of the Encyclopaedia Britannica.
Despite challenges in her youth, she showcased her brilliance in the Ask Marilyn column, solving complex puzzles and sparking debates.
đŹ The Monty Hall Problem: A Lesson in Logic and Resilience
Marilynâs story isnât just about winning the debateâitâs about challenging popular beliefs and standing firm in the face of criticism. Her resilience shows us the importance of logic and the courage to question the obvious, even when facing widespread doubt.
â Do you agree with Marilynâs answer?
Is switching the right strategy, or do you think thereâs more to the puzzle than meets the eye? Let us know your thoughts below and join the conversation!
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