Here’s a question for you:
John has two children. At least one of them is a boy.
What’s the probability that the other child is a girl?
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Decide on an answer before moving on.
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Ready?
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Ok!
Intuitively, most people would guess that there’s a 50% chance that the other child is a girl.
If that’s your guess, keep reading, because that’s the wrong answer.
Answer: 66% Probability
Here’s how it works.
With two existing children, there are four possible scenarios:
- Boy & Boy (BB)
- Girl & Girl (GG)
- Boy & Girl (BG)
- Girl & Boy (GB)
Now since we know that John has at least one boy, we can eliminate the second scenario and have 3 possible outcomes:
- Boy & Boy (BB)
- Boy & Girl (BG)
- Girl & Boy (GB)
Among these 3 outcomes, 2 of them include a girl. So the answer is 2/3, or 66%.
Asking The Right Question
This answer might seem weird because although the question is:
Given two children with at least one of them being a boy, what’s the probability that the other child is a girl?
… you might have been thinking of this question instead:
What’s the probability of a parent having a baby girl?
The answer to the first question is 66%, while the answer to the second question is 50%.
This small example highlights the importance of understanding the question before looking for the answer.
Good Questions Are Hard To Find
People are often busy trying to find answers, but few question whether they truly understand the question they are asking.
Why is this important?
Because unless you understand the question, you wouldn’t recognize the right answer even if it were right in front of you.
Worse, you may think you have the right answer, when it is actually the right answer to a different question.
Not sure what your point is. Hence I am unable to determine whether it is helpful to forex trading. If you go any further with this, it would be helpful to define what is “right” in this context. Helpful in what sense? Factual? Moral? Financial (as in outcome)? Confidence? Process?
Hi Rob, the point is to understand what you’re trying to do by examining the question you’re trying to answer. This applies to everything we try to do.
Chris, sometimes examining the question only leads to more and more questions.
Yes, it sometimes does. But usually, if you ask the right question(s), no further questions are needed…
Chris,
I put the same question to my two sons Fred & Divine. Their answer was 50% however i explained to them before they understood.
I totally agree with you that a lot of us do not understand the question before providing answers however its not possible that every one should understand or what do you think.
Hi Berthram, my opinion is that in understanding the question, the person that benefits the most is the questioner.
I think that everyone should understand the question they are seeking answers to, but of course not everyone will.
I sure hope your sons learned something new that day!
Hi Chris, you have given us a scenario what the outcome may be, which were 4 possible combinations. If you examine the combinations closely, you will find that combination 3 and 4 are exactly the same, no matter how you view the combination, which means that one of these can be scrapped. This leaves 3 possible combinations. By removing the girl and girl combination as that cannot be the case, you are left with two combinations. Thus, it could be either one of the two which is 50%. I agree that to get to the right answer you need to ask the right question but the person who receives the question must understand your thinking process to provide you with the answer that you want, whether it is correct or not. In your case with your logic 66% is correct but if you look at reality, it is 50%. Am I wrong in my thoughts?
Hi Frank, good question! This is an issue regarding permutations, and you can read more about it here if you’d like.
If you re-imagine the problem as two coins, one of which is Heads, the probability that the other is a tail has to be, in reality, 2/3 – similarly discounting the Tail/Tail combination.
Yes, exactly. Good example!