Those calculations that dominate our destiny.
Editor’s note: This article from the micro-channel public number “lonely brain” (ID: lonelybrain) , The author’s old Yu is in Canada.
First of all, the smart person you want to faint must be really smart;
Secondly, the one you use to confuse him must be a problem that looks less complicated.
In order to reduce the moral pressure of writing, I directly selected a topic that has already fainted a lot of smart people.
In fact, in the Internet age, it has been difficult to have any controversial and rigorous questions.
However, the question I am going to say is not only on the Internet, but also among the top academic experts.
Let’s get started right away.
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Mondino has co-authored “A Brief History of Time” with Hawking, and his “The Steps of the Drunk” is a great book about probability and randomness.
When it comes to the concept of “sample space,” Monrodino has a question:
Title A: Boys and Girls
A family of two children, the probability of having a male and a female is the same, and one is known as a girl.
What is the probability that another girl is also a girl?
This question seems to be very simple:
A girl is known to be a girl, the other is either a boy or a girl. The answer should be 1/2?
Answer: According to the concept of sample space, that is, I Why are really smart people probabilistic? (The introduction of the zero formula) said “parallel universe”, with the exhaustive method, the two children have the following four possibilities —
So, there is one known to be a girl, so the first possibility is excluded, and there are three possibilities, the answer is 1/3. The schematic is as follows:
For the confusing aspects of this question, Monlodino explained: If we specify which one is a girl, for example, the boss is a girl, then the probability of another girl is 50%.
As shown above: Because once the boss is appointed as a girl, the above four possibilities, the “male-male” and “male-female” may be removed from the sample space, so that only “female – Male and “female-female”, so the probability of “female-female” is 50%.
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However, another smart person “does not agree” with this answer.
He is Gary Smith, a Ph.D. at Yale University. He taught at Yale University for seven years and won two teaching awards.
In his book “Simple Statistics,” he criticized Monrodino’s “fallacy” by name.
Gary Smith presented the topic in another way:
Title B: Another child
A man named Smith is walking with his daughter.
Smith said that they still have a child in their family.
Excuse me: What is the probability that this child who is not around is a girl?
It seems that the expression of this question seems to be “similar” to that of Monrodino, but Gary Smith has a completely different answer.
First of all, he relentlessly criticized the “one-third” of the “experts” for the wrong answer.
Gary Smith gave a form:
