You know, I recently came across a story that perfectly illustrates why intuition often misleads us when it comes to probability. It's about Marilyn vos Savant and her famous answer to the Monty Hall problem.

It all started in 1990, when Marilyn vos Savant, known for her exceptional intelligence (her IQ was estimated at 228), published a solution to the classic paradox in her column for Parade Magazine. The game participant is offered to choose one of three doors—behind one is a car, behind the other two are goats. After the initial choice, the host opens one of the remaining doors to reveal a goat. The question is: should you switch your initial choice?

Marilyn vos Savant simply answered: yes, you should switch. And that’s when the controversy began. The editorial received over 10,000 letters, nearly a thousand of them from people with doctoral degrees. 90% insisted that Marilyn vos Savant was wrong. It seemed obvious that the probabilities were equal, but that was a mistake.

Why was she right? It all comes down to mathematics. When you initially choose a door, the probability that you picked the car is 1/3. The probability that the car is behind one of the other two doors is 2/3. When the host opens a door with a goat, he does not change these probabilities. If you switch your choice, you are essentially moving to the side of those 2/3.

Later, computer simulations by MIT and experiments by MythBusters confirmed Marilyn vos Savant’s correctness. The paradox became a classic example of how logic can contradict our intuition.

Marilyn vos Savant’s story itself is interesting—she faced serious challenges in childhood, including having to leave university to help with the family business. But it was her analytical thinking that allowed her to see what thousands of others missed.

This case demonstrates the huge gap between intuition and strict logic. The Monty Hall problem remains one of the most vivid examples of why we should trust mathematics, even when it contradicts our first impressions.