Behind one is a car 🚗. Behind the other two are goats 🐐.
You pick a door. The gameshow host opens another, revealing a goat.
You can choose to stay with your original choice or switch. What should you do? [Give it a try!].
The Monty Hall problem became famous when a columnist, Marilyn vos Savant, known as the world’s smartest woman, said you should switch, resulting in hundreds of letters, including from the brightest minds in mathematics, arguing she was wrong.
This engrossing article by Steven Pinker shines a bright light on this dilemma.
“People’s insensitivity to this lucrative but esoteric information pinpoints the cognitive weakness at the heart of the puzzle: we confuse probability with propensity.”
“A propensity is the disposition of an object to act in certain ways. Intuitions about propensities are a major part of our mental models of the world.“
Probability is “the strength of one’s belief in an unknown state of affairs“
“The dependence of probability on ethereal knowledge rather than just physical makeup helps explain why people fail at the dilemma.“
“They intuit the propensities for the car to have ended up behind the different doors, and they know that opening a door could not have changed those propensities. But probabilities are not about the world; they’re about our ignorance of the world. New information reduces our ignorance and changes the probability.“
