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Math Stats

Why Improbable Things Really Aren't 166

First time accepted submitter sixoh1 writes "Scientific American has an excellent summary of a new book 'The Improbabilty Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day' by David J. Hand. The summary offers a quick way to relate statistical math (something that's really hard to intuit) to our daily experiences with unlikely events. The simple equations here make it easier to understand that improbable things really are not so improbable, which Hand call the 'Improbability Principle:' 'How can a huge number of opportunities occur without people realizing they are there? The law of combinations, a related strand of the Improbability Principle, points the way. It says: the number of combinations of interacting elements increases exponentially with the number of elements. The 'birthday problem' is a well-known example. Now if only we could harness this to make an infinite improbability drive!"
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Why Improbable Things Really Aren't

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  • by Anonymous Coward on Tuesday February 18, 2014 @04:19AM (#46274055)

    The day before Fukashima happened I was writing a paper for an Industrial Safety class on the subject of Nuclear safety. My conclusion essentially made the argument that "Although individual improbable events are unlikely, the shear number of opportunities to experience an improbable event on a day to day basis are staggering." Any specific improbable event is highly unlikely to occur, but the occurrence of improbable events in general is a practical certainty.

    The next day I saw on the news that mother nature had done her best to prove my point. The timing worked out to be an incredibly unlikely coincidence, but on a daily basis I rarely notice when unlikely coincidences fail to occur. :)

  • by Trax3001BBS ( 2368736 ) on Tuesday February 18, 2014 @05:41AM (#46274243) Homepage Journal

    Very interesting article on it [] been a long time since I've read it (bookmark), but this guy can tell which scratch tickets will pay off by by reading their serial numbers, winning wasn't as improbable as one is led to believe - and yes, of course he's a statistician.

    I don't play the lottery, maybe a ticket twice a year, but my son likes the scratch tickets, I told him that they were predictable, he refused to listen; he wouldn't even pick up the link I printed out. He refused to imagine that it wasn't anything but random. It was just an odd reaction, I can't begin to explain the reasoning behind it.

    The link is old so I imagine the serial number gig has been fixed (yet I have no clue one way or the other), but supports the improbability disclaimer.

  • Oblig XKCD (Score:3, Interesting)

    by Anonymous Coward on Tuesday February 18, 2014 @06:06AM (#46274279)
  • by ph1ll ( 587130 ) <> on Tuesday February 18, 2014 @08:00AM (#46274495)

    Another example is in the curious case of Professor Meadows [] - a great paediatrician but a shite mathematician.

    He endorsed the dictum that “one sudden infant death is a tragedy, two is suspicious and three is murder, until proved otherwise“. The trouble is, given enough numbers, multiple cot deaths are an inevitability.

    Unfortunately, his expert testimony convicted an innocent woman. Fortunately, she was released on appeal when the math was reviewed.

  • by AthanasiusKircher ( 1333179 ) on Tuesday February 18, 2014 @09:58AM (#46274987)

    The link is old so I imagine the serial number gig has been fixed (yet I have no clue one way or the other), but supports the improbability disclaimer.

    While this may be interesting to some, it has very little to do with TFA.

    TFA is arguing that random events are often more probable than we might think, because we often fail to take the context of an event into account.

    Most of the scenarios in TFA are variations on the "birthday paradox," which basically amounts to people looking at an event X with a very tiny probability P in a specific case, and assuming that P is the probability it would happen. But we often forget that there are Q number of combinations or situations that would all result in X being true... so P is a gross underesimate of the probability of X.

    Your link deals with a poorly designed computer algorithm that actually isn't random which is spitting out lottery tickets. The scratch-ticket system has to make money, so the numbers can't be entirely random -- they must only payout so many tickets within a given batch. The guys who designed the computer system that chooses the numbers didn't take into account that there were statistical clues that could allow someone to "crack the code" to the fake randomness.

    There are two completely different phenomena. Finding a flaw in pseudo-randomness is completely different from miscalculating odds of genuinely random events.

No problem is so large it can't be fit in somewhere.