No, you are wrong!
The question of the problem is "What's the probability that my other child is a boy?"
The day of the week is irrelevant to the question, irrelevant to the answer.
It is not a matter of preconceptions, it is a matter of mathematics, elementary mathematics. If I tell you "I have a red square with a side of 1m. It is important that the square is not blue. What is the area of the square?". The answer is 1m^2 and has nothing to do with color. I am just trying to trick you. It might be important for aesthetic reasons that the square is red, so I am not lying to you, but this information has nothing to do with the area.
Did you notice the word "magicians" in the original story? That's the key. It's a very simple problem in mathematics, BUT the magician tries to confuse you. It is really elementary. And apparently it works with a lot of people. That's very interesting!
And let me point again that it is wrong to mix joint probabilities when you don't have too.
In the example I gave above, you arrive to the correct conclusion by giving one to the probability of the first child to be a boy.
However, it is wrong and stupid to compute JOINT probabilities, what what you want is single probabilities. If nothing else, you may have no way to compute the joint probability!
For example, if you state "I have two children, one of whom is a boy born during a storm. What's the probability that my other child is a boy?"
Well, it is 0.5, you do not have to compute any joint probabilities. Because obviously the storm does not influence the gender of the child in question. It does not even influence the gender of the first child! It is just irrelevant information. It is just like saying:
"I have two children, one of whom is a boy and I like ice cream. What's the probability that my other child is a boy?"
Both you and the other user (Xest), confuse joint probabilities for multiple independent events, with probabilities for a single independent event. The probability of a single independent event does not change. This is elementary probability theory.
Perhaps a simple example will help you. Let's say that your wife is pregnant with your first child. The probability to be a boy is 0.5. The child is born and it is really a boy. Congratulations! Now the probability to be a girl is zero! Some years later your wife is pregnant again. What is the probability to have again a boy? Well, it is again 0.5! Some assume that we have to multiply 0.5*0.5=0.25. No, that's wrong! The probability for the first child to be a boy is now 1 (one!) since it is a known fact! The probability for the first child to be a girl is zero. So, even if you want to multiply, you should do 1*0.5=0.5 and you get the same result.
However, this way of thinking is wrong anyway, because it is confusing. We do not have joint probabilities here. There is no way that a previous child can influence the gender of the next child. You should not multiply anything because there is no causal relationship. It does not matter if it is your first, second or tenth child. There is always probability 0.5 for the next child, no matter how many children the woman had before. This is common sense, and it is also formal mathematics.
It is different when you want to compute JOINT probabilities, that is TWO or more events to happen simultaneously. Yes, the probability to have two boys is 0.25. But if you KNOW that one is a boy, then you do not have joint probabilities any more. You just have the probability for one child to be a boy, that's 0.5. If you insist to use joint probabilities, then you have to multiply by one 1*0.5=0.5. It is a completely different question to ask "what is the probability for two random human beings to be two males?" and different if you ask "what is the probability for one random human being to be a male?". The second question has always probability 0.5, since it's a random human being.
The problem as it was stated was full of mistakes. Probably intentional, to confuse the readers and generate discussion. There is no trick at all, it is just bad mathematics.
Yes, exactly! The probability of your next flip being heads is also 1 in 2!
It does not matter what happened in the past, the probability of those events are now 1 (one!) and do not influence future events.
You are right that "the probability of flipping a coin and getting heads 11 times in a row is 1 in 2048". But, this is the joint probability for multiple events to occur. However, each flip coin has probability of 0.5. No matter how many coins you have flipped before, no matter how many coins you will flip after.
That's elementary statistics. Please ask any professor. I used to teach probabilities in the past.
No, it does not. It is the trick of a magician to draw your attention to irrelevant information. And to lie to you.
The ratio 1/3 is also wrong. If the youngest is a boy, then the probability for the oldest to be a boy is 1/2. Because those things are completely independent. You do not have joint probabilities in this problem. It does not matter if the youngest is boy, girl, older, younger, black or white
This is similar to "gambler's fallacy". Look it up!
No, the ambiguity is completely irrelevant.
It doesn't matter what day the boy was born. It doesn't matter what month, what time, if it was raining etc.
Those things have nothing to do with the genre of either child.
It is a flaw in the original article.
The question is about the genre of the other child, no matter what day it was born. So, the days are irrelevant. It's meaningless to multiply irrelevant data.
If the question was "What is the probability the other child is a boy born on a Sunday", then days would be relevant.
The author misleads the audience, like a magician. The whole problem is just a trick for people who know nothing about statistics. Statistics 101 says: do not mix uncorrelated data!
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