Hi guys
Sorry if this question's been asked, but can somebody please explain to me the concept/intuition behind solving probability using symmetry?
OG Diag Q7 is an example of a question that can be answered using symmetry (according to OG Navigator), but I can't seem to wrap my head around the intuition
Can somebody please help me figure this out or point me to a resource that explains it well?
Thanks!
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- sherifabdulla
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- RonPurewal
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Re: Probability symmetry
The idea here is, basically, "If two people/things are in the same situation, then the probabilities are the same."
In the problem you mentioned (thanks for not quoting it, by the way"”OG can't be quoted here), the point is that there is nothing special about "Harry"; he is in exactly the same situation as each of the other nine people. So, each person has exactly 1/10 chance of being chosen for either position.
As far as resources are concerned, your best bet is probably just to search the internet for "probability symmetry" or other such search terms. I'm sure there are pages out there.
In the problem you mentioned (thanks for not quoting it, by the way"”OG can't be quoted here), the point is that there is nothing special about "Harry"; he is in exactly the same situation as each of the other nine people. So, each person has exactly 1/10 chance of being chosen for either position.
As far as resources are concerned, your best bet is probably just to search the internet for "probability symmetry" or other such search terms. I'm sure there are pages out there.
- sherifabdulla
- Course Students
- Posts: 5
- Joined: Tue Feb 04, 2014 6:28 am
Re: Probability symmetry
Thanks Ron
I get the idea of Harry not being "special", but then how can we say that "each person has exactly 1/10 chance of being chosen for either position"? Why do we no longer need to consider that if one person is chosen for one position, then probability of Harry being chosen for the second position goes up?
I get the idea of Harry not being "special", but then how can we say that "each person has exactly 1/10 chance of being chosen for either position"? Why do we no longer need to consider that if one person is chosen for one position, then probability of Harry being chosen for the second position goes up?
- RonPurewal
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Re: Probability symmetry
Right, but, the same thing is still true for everyone else, too.
In other words, consider each of the following questions:
What is the probabliity that Person #1 is chosen for the second position?
What is the probabliity that Person #2 is chosen for the second position?
What is the probabliity that Person #3 is chosen for the second position?
Etc.
It should be clear that the answer has to be the same for all of these questions, so the answer must be 1/10 for each of them.
In fact, this kind of thing is the only real utility of thinking about this kind of "symmetry". If we were just thinking about things like choosing the first position, then the symmetry argument would just yield results that were already obvious.
In other words, consider each of the following questions:
What is the probabliity that Person #1 is chosen for the second position?
What is the probabliity that Person #2 is chosen for the second position?
What is the probabliity that Person #3 is chosen for the second position?
Etc.
It should be clear that the answer has to be the same for all of these questions, so the answer must be 1/10 for each of them.
In fact, this kind of thing is the only real utility of thinking about this kind of "symmetry". If we were just thinking about things like choosing the first position, then the symmetry argument would just yield results that were already obvious.
4 posts Page 1 of 1