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Marilyn Firth Savant's Monty Hall Paradox
In the early 1990s, Marilyn Firth Savant was notorious for answering the "Monty Hall Paradox". Monty Hall prom, also known as Monty Hall Problem or Three-door Problem (English: MontyHallprob-lem), is a mathematical game problem originated from game theory, which is roughly derived from the American TV game show Let's Smakeadeal. The name of the question comes from the program host Monty Hall. The game is played like this: the contestants will see three closed doors, and there is a car behind one of them. Choose the door with a car behind it to win the car, while the other two doors hide a goat behind them. When a contestant chooses a door (suppose it is 1) but it doesn't open, the host will open one of the remaining two doors (suppose it is Gate 3) to reveal one of the goats. Then the host will ask the contestants if they want to change another door that is still closed (Gate 2). 1On September 9th, 990, a reader named Craig Vitca wrote to Savant, asking: Will changing Gate 2 increase the chances of the contestants winning the car?

Savant replied that another door is more likely to win the prize. This answer caused a strong response. Thousands of letters of complaint followed. There are many math teachers and scholars among the protesters. A reader of the University of Florida said, "There are too many math illiteracy in this country, and we don't need people with the highest IQ in the world to make more such fools. Shame! " Another reader insulted and said, "You are a goat!" Everett Harman, a reader of the US Naval Research Institute, wrote, "You made a mistake, but on the bright side, if those doctors of science are wrong, then this country is in trouble."

However, Savant was not wrong. Finally, she used four columns to explain that a class of children did experiments in class. After hundreds of news reports, she finally convinced her readers that she was right. "That's interesting. I especially like reading letters of protest full of resentment, "she said. "Those who are bold and shameless! I really love them. "

The key to solve this problem is the host, who always can't pick the door behind the prize. According to the statistics of the game results, those players who choose to change doors are twice as likely to win the prize as those who don't. Savant explained in the third column: "When you first choose the door 1 from the three doors, the probability of a car behind it is 1/3, while the probability of a prize behind the other two doors is 2/3. But this time the host came out to give you a new clue. If the prize is behind Gate 2, the host will show you Gate 3. If the prize is behind Gate 3, he will open Gate 2. So choose to change doors, and the prize will win after Gate 2 or Gate 3. But if you don't change the door, you can only win the prize if the prize is behind 1 door. "