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Comments

• [1] Chris August 11, 2009 - 03:14PM

  Actually, I believe that the likelihood of getting a run of 7 tails in a row, over 100 flips total, is just over 50%. In 100 coinflips, you're looking at 93 (or 94, I'm not sure right now) sequences of 7, any one of which could be a run of 7 (I'm also granting the possibility of a run of 7 being preceded by a tails or followed by one, so technically I quoted the chance of a run of 7 or more), so the chance of NOT finding a run of 7 is (1-.5^7)^93, or approximately 48%.

  I realize, statistically speaking, I'm somewhat ignoring icky things like independence, but I'm still fairly certain that I'm in the right ballpark.

  
  
• [2] Alan September 05, 2009 - 05:29PM

  Great show guys. I teach a graduate methods course in psychology and I think I will use of some of these clips to illustrate the tendency for people to see patterns when there is (mostly) just randomness. By the way, if any listeners of your show are interested in learning more about things like the "hot hand illusion" and other errors of perception covered in this segment, Amos Tversky and Tom Gilovich did a lot of great work on these issues, much of which is summarized in very readable form in Tom's book, How We Know What Isn't So. (NB I have no connection whatsoever to that book or its authors or profits; etc.)

  
  
• [3] Michael Shulman September 12, 2009 - 01:42AM

  @Chris,

  I agree with you. The error was distracting me from the rest of the show.

  But isn't the probability really (1-0.5^7) * 93 == 73%

  (1-0.5^7) ^ 93 == 1.07e-196

  -ms

  
  
• [4] Mills from Virginia, USA September 22, 2009 - 09:34AM

  These sorts of coincidences are very seductive which is why, I think, they survive in our culture. As an example, this summer my father passed away on July 20 and his funeral arrangements were handled by Murphy Funeral Home here in Virginia. While clearing out his house, I found his mother's death certificate. She died in the 1980s -- on July 20 and her funeral arrangements were handled by Murphy Funeral Home, but in California.

  I asked my father-in-law, who is far better at mathematics than I, what the odds were of this sort of coincidence. His response was that the probability was almost certainly between 0 and 1. Okay, I knew that much.

  Thanks for the great show.

  
  
• [5] EERac from New York, NY October 05, 2009 - 03:41PM

  I was just listening to the podcast of this episode and googled this page to see if other folks were bothered by the claim that there was only a 1/6th chance of a run of 7 tails (or heads). The claim is definitely way off, but (1-.5^7)^93 isn't correct either.

  Any given run of 7 flips has probability .5^6 of being either all heads or all tails. In the show, they seem to divide the 100 flips into 14 separate chunks of 7 runs, and note that the probability that they all fail is only (1 - .5^6)^14 which is around a 80 percent. The thing is, that's way too pessimistic. Anytime you're flipping the coin, and you switch sides, you have a new shot at a 7 flip run.

  On average, runs last for 2 flips, so you'll get about 46 shots at a 7 flips run. As far as I can tell, it's cumbersome to work out the exact probability, but a conservative estimate would to assume you'll have 40 chance to get 7 in a row. This would give a probability of .47 that you'd get a 7 flip run.

  Honestly, it's pretty disappointing that an actual statistician got this so wrong. A simple check, if the radiolab folks want to correct themselves, would be to just run a few 1000 computer simulations.

  
  
• [6] Irene Cardenas from Minneapolis, MN October 05, 2009 - 04:15PM

  How about connections in energy fields, including thought fields, causing coalescing or amplified vibrations that some people think of as co-incidence? Think of what that term, "co-incidence" means in terms of waves in physics. Actually, physical waves of energy co-incide, as many physicists know. Waves of energy fields from all things made of electron fields can go on infinitely, capable of interacting with everything we know on earth.

  "Hot hand" can be the momentum of the effective energy flow pattern coursing through neural impulses in muscles and the brain (vision/motor coordination). Neural patterns reinforce and repeat themselves. There's a biological basis. Radiolab did a show about how energy pulses through the neural system before a person is conscious of making his own decision. The holistic perspective (right-brained/feminine) is different than the reductionist perspective (left-brained/masculine), which thinks everything is separate (the belief in ego) and random.

  
  
• [7] Terry Hayes from Lexington, Ky. October 10, 2009 - 01:37PM

  I just listended to show on stocasticity recently and thought it was cool enough, until you got to the end and started going all gooey. The part where you spoke about how individual single celled organisms turned on protiens randomely and so forth and started talking about the "mystery" of how that low level randomeness turns into order at higher levels.

  I don't really see the mystery here and think that if you had just spoken to that statistician you talked with earlier you might have had a less touchey feely ending about how people are unpredictable blah, blah, blah and just given a randomeness.

  If you want to see how a randome item can produce order on higher levels try this.

  Roll a single dice one time, a hundred times. Looking at the string of numbers you see randome strings of numbers.

  If you roll a simple dice a millions times each single time will be a randome time. If you look at any short sequence of numbers generated so you will see randomeness. But if you AVERAGE those numbers you will get order. With just a few trials you will get a randome number that could be anything between 1 and 6, but will be closer and closer to 3.5 with many trials.

  Eventually, with millions of trials you will get 3.5 almost exactly. Thus, millions of cells in a single organisme or a single cell doing something it does millions of time, will produce a rather orderly total.

  You really should work harder at being a Radio LAB and not a radio - place that talks about science. There are enough ACTUAL mysteries out there that inventing them to contrive some sort of poetic ending to your show is not science, and thus does not belong in a lab.

  
  
• [8] Truman Buffett from Seattle, WA November 14, 2009 - 03:53AM

  Oh No!

  It's great to hear MATH on the radio, but how did a calculation that's so far from being correct ever make it through to the final edit? The probability of getting a string of 7 (or more) tails in 100 flips is ~31.752%. The probability of getting a string of 7 (or more) tails OR a string of 7 (or more) heads in 100 flips is ~54.234%.

  I used an absorbing Markov chain to find these. Using a TI-83, it took about a minute to solve each. I'll try to come back soon and post a more detailed description of a method to find these numbers. Sullivan and Mizrahi's "Finite Mathematics" is available used for less than a buck at Amazon; they tell you everything you need to know about Markov Chains.

  
  
• [9] Yanming from Corvallis November 17, 2009 - 02:49AM

  I don't know how to derive that probability easily, but I simulated 100000 sets of 100 coin flips: According to my simulation, the probablity of getting at least 7 tails in a row should be about 0.316. So I will trust Truman above.

  
  
• [10] Truman Buffett from Seattle, WA November 17, 2009 - 10:00PM

  In brief, the probability of such an event occurring is given by the ninth entry in the 1x9 row vector vP^100. Where v = [1, 0, 0, 0, 0, 0, 0, 0, 0] and P is the 9x9 matrix with p_(1,2)=p_(1,3)=.5, and p_(k,2)=p_(k,k+1)=.5 for k=2...8, and p_(9,9)=1 and all other entries zero.

  I know this seems dense, but if you send me a message on Facebook (I'm the only "Truman Buffett" with a profile picture) I'll send you a link to a video that will walk you through the problem and the method used above.

  
  
• [11] Gina Mireault from Vermont November 22, 2009 - 09:21PM

  I also teach Research Methods in Psychology as well as Developmental Psychology. In the latter, we explore the "uncanny" similarities between between identical twins who are reared apart. Researchers make the assumption that these similarities (e.g., using the same unusual toothpaste or drinking the same brand of beer) are genetically based, even though they would not apply such explanations to the same similarities found between total strangers (like the Laura's in this edition of RL). I'll use this segment in class to illustrate that coincidence works as a third variable in explaining such similarities, as well as to discuss the human tendency to "see patterns in randomness". Thanks for an outstanding show!