In 1990, Marilyn vos Savant correctly answered a probability puzzle in her column for Parade Magazine. And then, the world called her an idiot.
I still remember the chaos caused by the Monty Hall problem in our high school math class. Here’s my explanation for how it works:
- Your first choice could either be a goat or a car.
- If you picked the car, you will win the car by not changing your guess.
- If it’s a goat, you will win the car by changing your guess.
- Since you’re twice as likely to have picked a goat than a car, you’ll be twice as likely to win by switching for your second guess.
Note that picking a goat and changing your guess will guarantee the car, since the host has revealed the second goat.
The best strategy is to try to pick a goat in round 1, and plan to switch once the host has revealed the second goat.