In September 1990, Marilyn vos Savant, widely recognized for holding the highest IQ ever recorded, sparked a heated debate that still fascinates mathematicians and the general public. Her response to the Monty Hall problem—a probability puzzle inspired by the famous game show Let’s Make a Deal—challenged conventional wisdom and ignited an uproar among readers, including academics.
The Puzzle: The Monty Hall Problem
Here’s the scenario:
• A contestant is presented with three doors. Behind one is a car, and behind the other two are goats.
• After the contestant selects a door, the host (who knows where the car is) reveals a goat behind one of the remaining doors.
• The contestant is then given a choice: stick with their original door or switch to the other unopened door.
The Question:
To maximize the chances of winning the car, should the contestant stick with their choice or switch doors?
Marilyn’s Answer: “Always Switch”
Marilyn’s response in her Parade Magazine column was clear: “Yes, you should switch.”
Her reasoning? Switching doors increases the chance of winning from 1/3 to 2/3.
The Backlash: A Storm of Criticism
The public reaction was explosive. Marilyn received over 10,000 letters, including nearly 1,000 from PhD holders, with 90% insisting she was wrong. Critics mocked her answer, claiming:
• “You completely misunderstood probability.”
• “This is the biggest blunder I’ve ever seen!”
• “Perhaps women don’t understand math like men do.”
Was She Wrong? Absolutely Not.
The Mathematical Explanation:
1️⃣ Initial Choice Probability:
• The chance of picking the car on the first try is 1/3.
• The chance of picking a goat is 2/3.
2️⃣ Impact of the Host’s Knowledge:
• If the contestant’s initial choice was a goat (2/3 probability), the host will always reveal the other goat. Switching in this scenario guarantees a win.
• If the initial choice was the car (1/3 probability), switching results in a loss.
3️⃣ Conclusion:
By switching, the contestant wins in 2 out of 3 scenarios, boosting the probability of success to 2/3.
Proof and Validation
Marilyn’s answer was later confirmed through:
• Computer Simulations: MIT and others ran thousands of trials, consistently showing a 2/3 win rate for switching.
• MythBusters: The popular show tested the problem and verified her explanation.
• Apologies from Academics: Many who initially criticized her later admitted their mistake.
Why It Feels Counterintuitive
1️⃣ Misjudging Probabilities: People assume that once a goat is revealed, the remaining doors each have a 50% chance, ignoring the original 1/3 and 2/3 probabilities.
2️⃣ Reset Bias: Many see the second choice as a new, unrelated event, when in fact it’s a continuation of the original probabilities.
3️⃣ Deceptive Simplicity: The small number of doors makes the problem feel simpler than it is, masking the underlying complexity.
Marilyn vos Savant: A Genius Ahead of Her Time
The Woman Behind the IQ of 228
• Recognized by Guinness World Records for her unmatched intelligence.
• By age 10, she had read all 24 volumes of the Encyclopaedia Britannica and memorized entire books.
Despite her intellect, Marilyn faced financial hardships growing up, dropping out of university to support her family. Her brilliance was later showcased in her Ask Marilyn column, where she tackled complex puzzles, earning admiration and criticism alike.
The Monty Hall Problem: A Lesson in Logic and Resilience
Marilyn’s experience with the Monty Hall problem is a powerful reminder of the gap between intuition and mathematics. Despite widespread ridicule, she stood by her answer, ultimately proving millions wrong and leaving a lasting legacy in probability theory.
Her story is a testament to the power of logic, perseverance, and the courage to challenge popular opinion—even when facing overwhelming doubt.