When an entire community assumes in a closed way that there is only one truth, it is difficult to convince them that there may be alternatives. Especially if we talk about mathematics, where the accounts are usually clear.
The approach is very simple. Imagine that you are in a television game show where the jackpot is a car. There are three doors and only one of them is the vehicle. You have to choose one. After expressing his choice, the presenter opens one of the doors -one of the discarded ones-, and it is empty.
After this, it allows you to choose again. Do you stick with the chosen door at first or would you change your mind? A priori, the probability of taking the car is 50%. However, a woman revolutionized the whole world after stating that, in reality, it is 66%, almost two thirds of probability.
This puzzle is known as the Monty Hall Problem. And the woman in question is American and studied Philosophy. Marilyn vos Savant was born in San Luis (USA) in 1946. She is considered the most intelligent woman in the world, since in one of the tests that measure the intelligence quotient she obtained a 228, a record admitted by the ‘Guinness Book’.
Vos Savant’s 1990 response to the Monty Hall Problem (published in his ‘Ask Marilyn’ column) sparked a barrage of letters (more than 10,000, according to the BBC), many of them critical of his approach.
“As a professional mathematician, I am very concerned about the general public’s lack of math skills. Please help by confessing your mistake and be more careful in the future,” said Robert Sachs, a professor at George Mason University in Virginia. .
“You are dead wrong,” wrote E. Ray Bob, a professor of mathematics at Georgetown University. “How many angry mathematicians does it take to change your mind?”
The answer is based on the premise that in the contest they will always show one of the doors without a prize after the first choice and that, in addition, they will allow you to choose another door again. Do you keep your door or change it?
“Yes, it should change,” said Vos Savant then, who reasoned it like this. “The first door has a one-third chance of winning, but the second door has a two-thirds chance. Suppose there are a million doors and you choose door number one. The contest host, who knows what’s behind the doors and will always avoid revealing the one with the prize, it opens all of them except door 777,777. You change the door fast, right?”
A few years ago, the BBC witnessed an experiment in which Cardiff University students divided themselves into presenters of the show and contestants.
Those who changed the answer were roughly twice as successful, as out of 30 contestants who decided to do so, 18 won the car. That is, there was a 60% hit rate. Meanwhile, of 30 who decided to keep their choice, there were only 11 correct answers, a rate of 36%.
The British chain assures that, after proving that she was right, she did not receive as many letters as in 1990, much less apologizing.
Except for Professor Sachs, who said: “I am now eating the humility pie. As a penance I promised to respond to all the people who wrote to reprimand me. This has been a profound professional embarrassment.”
According to the criteria of The Trust Project