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OT: probability calculations

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  • MattiJ
    replied
    Originally posted by J Tiers View Post
    I expect this is leading up to the problem of antibody testing.
    -------
    This would be different if a LOT of people were exposed, then the test would be reasonably workable.
    You saved me trouble and explained the point better than I probably could have done. And it is interesting "tricky question" on its own.

    Forum members were not enough easy to lure to trap...
    Last edited by MattiJ; 05-08-2020, 05:51 AM.

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  • dian
    replied
    Originally posted by J Tiers View Post
    I expect this is leading up to the problem of antibody testing. Much is made of antibiody testing, and "coronavirus passports" that show the person is (maybe) now "immune" so they are safe and supposedly are also not a danger to others and can move about freely (of course we do not know that is possible, but never mind that).

    Suppose you have a test that is 95% accurate, that is it ALWAYS identifies actual antibodies, but it gives a false positive 5% of the time for people who actually have NO antibodies. So only 5% of the tests on unexposed persons will suggest that they WERE exposed.

    That seems pretty good, pretty good accuracy, and it should be good to go, right?

    Now 1000 people take the test, and suppose 3% of them have been exposed. So you have 30 people who show up with antibodies, and 970 people who do not have antibodies.

    So what do you get as a result?

    You get 78 people identified as being "safe", 48 of whom are totally unprotected but would be allowed to go around freely, catching the virus and spreading it. You actually have more false positives than true ones.

    So the test that "looks pretty good", is in fact pretty nearly useless.

    Even if 10% had been exposed, still almost 1/3 of the "OK" people would actually be totally unprotected.

    This would be different if a LOT of people were exposed, then the test would be reasonably workable.
    thank you for explaining what i said in post #7.

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  • elf
    replied
    Originally posted by Erich View Post
    The problem boils down to one of two choices.

    First, Pick a door any door. There is a wonderful prize behind one door and a goat behind the other two.
    Now Here is you second choice. Would you trade your door for BOTH of the other doors?

    Hmmm Do I want one chance to win or two chances to win? I know, give me the second choice. I want two chances to win. The fact that one of the doors not chosen at first is shown to have a goat is irrelevant. You knew that going in. Because there are either two goats in them or one goat.
    What if you really wanted a goat because you were tired of mowing your lawn?

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  • J Tiers
    replied
    I expect this is leading up to the problem of antibody testing. Much is made of antibiody testing, and "coronavirus passports" that show the person is (maybe) now "immune" so they are safe and supposedly are also not a danger to others and can move about freely (of course we do not know that is possible, but never mind that).

    Suppose you have a test that is 95% accurate, that is it ALWAYS identifies actual antibodies, but it gives a false positive 5% of the time for people who actually have NO antibodies. So only 5% of the tests on unexposed persons will suggest that they WERE exposed.

    That seems pretty good, pretty good accuracy, and it should be good to go, right?

    Now 1000 people take the test, and suppose 3% of them have been exposed. So you have 30 people who show up with antibodies, and 970 people who do not have antibodies.

    So what do you get as a result?

    You get 78 people identified as being "safe", 48 of whom are totally unprotected but would be allowed to go around freely, catching the virus and spreading it. You actually have more false positives than true ones.

    So the test that "looks pretty good", is in fact pretty nearly useless.

    Even if 10% had been exposed, still almost 1/3 of the "OK" people would actually be totally unprotected.

    This would be different if a LOT of people were exposed, then the test would be reasonably workable.
    Last edited by J Tiers; 05-08-2020, 01:02 AM.

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  • Erich
    replied
    The problem boils down to one of two choices.

    First, Pick a door any door. There is a wonderful prize behind one door and a goat behind the other two.
    Now Here is you second choice. Would you trade your door for BOTH of the other doors?

    Hmmm Do I want one chance to win or two chances to win? I know, give me the second choice. I want two chances to win. The fact that one of the doors not chosen at first is shown to have a goat is irrelevant. You knew that going in. Because there are either two goats in them or one goat.

    Leave a comment:


  • ed_h
    replied
    The relationship between the statistics problem and the TV show is pretty incidental. Someone applied the name of the show to the problem because it is a real world example, but the problem would still exist even if the show never had.

    Ed

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  • Paul Alciatore
    replied
    Not if the host's choices are either truly random or if they follow a fixed pattern.

    I suspect that those choices are not even the actual host's choice. Having been behind the scenes in many TV productions, I would suspect that he is told which door to open by someone behind the scenes. And that choice can be made in any of several ways. This could also be conveyed to him, on the fly, in a number of ways. For instance, in any TV production there is always a person who is called a Floor Director. This is a person who is on the studio floor, somewhere between the cameras and who is connected to the Director in the control room with a headset. He/she literally conveys the actual show director's directions to the host and others in the program, usually with hand signals that they watch for. That Floor Director could simply hold up one, two, or three fingers to signal which door to open first. If that is the case, then the show's host really does not need to even know which door is the winning one. That would prevent the host from giving any unintentional signals to the contestant. And that is how I would set it up.



    Originally posted by lynnl View Post
    The Monty Hall problem starts off as a probability question, and then the solution offered is mainly a psychology one.
    A classic case of obfuscation!
    Last edited by Paul Alciatore; 05-07-2020, 05:54 PM.

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  • ed_h
    replied
    Originally posted by lynnl View Post
    The Monty Hall problem starts off as a probability question, and then the solution offered is mainly a psychology one.
    A classic case of obfuscation!
    No, not at all. The solution is objective, provable, and testable.

    Ed

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  • lynnl
    replied
    The Monty Hall problem starts off as a probability question, and then the solution offered is mainly a psychology one.
    A classic case of obfuscation!

    Leave a comment:


  • dian
    replied
    such stuff is not the main problem of statistics. the main problem of statistics is that they are statistically insignificant in almost all cases. (since you mention corona testing.)
    Last edited by dian; 05-07-2020, 02:46 PM.

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  • Mcgyver
    replied
    Now if you had three cats in three boxes and you opened one and the cat was ____________ .......

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  • QSIMDO
    replied
    Aw, c'mon, I'm still struggling over Schrodinger's Cat.

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  • ed_h
    replied
    Yes, it's the well known and much discussed Monty Hall problem. The answer is non-intuitive to most.

    Ed
    Last edited by ed_h; 05-07-2020, 11:19 AM.

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  • MattiJ
    replied
    Spoiler :P

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  • mklotz
    replied
    Monty Hall problem...

    https://en.wikipedia.org/wiki/Monty_Hall_problem

    Leave a comment:

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