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A Very Lucky Wind

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Laura Buxton, an English girl just shy of ten years old, didn't realize the strange course her life would take after her red balloon was swept away into the sky. It drifted south over England, bearing a small label that said, "Please send back to Laura Buxton." What happened next is something you just couldn't make up - well, you could, but you'd be accused of being absolutely, completely, appallingly unrealistic.

On a journey to find out how we should think about Laura's story, and luck and chance more generally, Jad and Robert join Deborah Nolan to perform a simple coin-toss experiment. And Jay Koehler, an expert in the role of probability and statistics in law and business, demystifies some of Jad and Robert's miraculous misconceptions.

Comments [58]

Peter from Oz

Using the coin tossing investigation as a comparison to the Lauras' story is like comparing a photo of planet Earth to planet Earth: trivialised.
There are only two possible outcomes with each coin toss. This should be enough clue to stop making comparisons there.
I would love to see a proper statistical evaluation of the Lauras' case, one that a layman can understand. I can see a number of probability factors that would need to be included in the analysis,such as -
what is the chance of:
1. two people having the same name AND attending same grade
2. a person with a nemesake somewhere else ever releasing a helium baloon
3. any helium baloon that has ever been released to have a name tag with address attached
4. a person with a nemesake somewhere else ever releasing a helium baloon with their name and address attached
5. any helium baloon being found by another person
6. any baloon with attached name and address being found by another person
in the proximity/vicinity of the sender's namesake
7. furthermore factor in probabilistically the dog, guinea pig, rabbits, the girls' dresses at meeting, the parents.

I am guessing the probability of this happening is ... I don't know. I want to say zero but it obviously is not! I think 'Irene Cardenas from Minneapolis' and 'Susan from Sea Cliff' are onto something of import.
faiglD.O.T.peterA.T.g-m-a-i-lD.O.T.c-o-m

Jul. 10 2014 07:17 AM
Kirby from Long Beach

The odds which are defied by this balloon going to a girl with the same name is next to zero. It amazes me how the world works in such mysterious ways, and you never know when the smallest things can have the biggest impact on you. Its a cool story because it is so unlikely to meet someone with the exact same name, interests, pets, and overall similarities you can find from attaching a card with your name to a balloon that it leaves me in awe how lucky some people like Laura Buxton are!

Jun. 16 2014 01:21 AM
Fiona from CA

This podcast was so amazing! It was incredible how two girls with the same name, age, hair, clothes, and pets found each other. In some crazy twist of fate that weird balloon brought them together, this has really charnded my views open the entire topic of probability and statistics. Out of seven billion people in the world, they found each other. Wow!

Jun. 07 2014 03:03 AM
Erin from CA

I was completely shocked by this podcast. It completely changed my point of view on probability. The outcome of this podcast is completely unexpected and astonishing. What are the odds that she would have the same name as well as physical characteristics, that's crazy! It completely shifted my point of view on the whole topic of probability and proves that literally anything is possible, no matter how farfetched it may seem. It has definitely made me aware that even though something may seem close to impossible, you never know the odds.

Jun. 05 2014 10:31 PM
Hailey Stenberg from Southern California

I thought that this podcast was such a crazy weird story. It was so interesting and unexpected that one girl named Laura Buxton could let go of a balloon with her name and address on it and have it travel across the country for it to land in the hands of another Laura Bruxton. It was also unepected to see all the similiarties they had from how they look and dressed to the type of animals they had and brought. I would have never thought that that the probabilty of a girl finding a balloon with her exact name but from a different address is crazy.

Jun. 05 2014 10:25 PM
Nick from Southern California

It's a fascinating story that could have gone many ways, but the fact that both of them just happened to be Laura Buxton is awesome. The thing that really opened my eyes was when they spoke to the man from Arizona State University and he explained to them that the odds of that happening were very unlikely, unless you factor in the things people overlook. Also, when they explained the people winning the lottery multiple times and how unlikely that is, until you factor in everything. I think it just goes to show that although things may not be very groundbreaking or special to someone, may actually be considered a miracle to others. So, all in all, always cherish the things you take pride in or love.

Jun. 04 2014 01:44 AM
Scott Thomas from California

The podcast was very interesting and made me think how things seem very unlikely, but finds a way. Even though things seem very unlikely there is always a chance of something may happening. In geometry if I see a circle that is divided in twelfths and only one of them were shaded, I would think to myself that it would be unlikely for it to be landed on. If I think of a girl who puts a balloon in the sky and it somehow lands on a girl who is practically the exact same person and with the same name I think of it as extremely unlikely. This proves that how anything is possible.

Jun. 03 2014 10:56 PM
Ashley Barnett from CA

I found this radiolab to be very interesting and informative. It was crazy how the first Laura Buxton who is quite tall with brown hair and who is ten years old could let go of a balloon and it be found by another ten year old with the same characteristics and the Name of Laura Buxton. It blows my mind to think that there is a pretty good probability that is i were to do the same someone just like me could find my balloon. This podcast was definitely unexpected and its has really changed my views on the probabilities that can occur.

Jun. 03 2014 01:02 AM
Nick Ursini from California

This podcast was very interesting. It really got me to look at the big picture which is the whole population rather than the one person. It kind of ruined miracles and chances for me because it did a good job explaining that if something is done over and over there is a greater chance of something "random" happening. I feel that it kind of put a little doubt about God. Many people said the probability of A planet having humans is the same as a monkey typing a Shakespere play word for word, but that does not into account about the huge amount of planets to sample to.

May. 21 2014 12:18 AM
Jourdan from Ca

i find it very interesting that for one, the two girls by chance just happen to find each other and just happen to have a lot in common. The other thing i find interesting is how they have two groups flip real coins and "fake coins". I am not quite still sure why they do that but its still entertaining to listen to. There is also a lot of conflict during the 100 coin flips when they receive seven tail in a row. But in the end if you work out everything mathematically its only 1/6 chance which i find that is should be a smaller number(just by listening to it w/ no math)

May. 20 2014 01:57 AM
Kiet Ho from His living room

Statistic just ruined miracles for me :(. But overall, its an interesting topic, showing that miraculous things are very likely to happen, not as impossible as we might think they are.

May. 19 2014 10:33 PM
graham

i loved this story! this was so amazing to me. Probability is such an intriguing thing! God definitely played a role in this. i was so surprised to see peoples view on probability.

May. 18 2014 11:06 PM

I thought that this was a very interesting story. What are the odds! I consider these as miracles. How do these thongs happen? I think its the work of God. I think the balloon got there by a push by God. These are miracles!

May. 17 2014 02:08 AM
Hannah Wessel

I thought that the broadcast was very interesting. It made me think about probability differently. The story of Laura Buxton was very interesting. That is so bizarre how she just left her balloon and it just so happened to land in the other hand of a person who has very similar characteristic, even including her name. It is just crazy to think that out of all the people in the world it would land in her hands. I also thought that what the probability people said was very interesting and I never thought of it that way

May. 17 2014 02:01 AM
Chloe Hovorka from CA

Personally, I loved this radio show. The story of the Laura Buxton girls is incredible, and before this expirament, I would have thought that the odds were one in a billion. It was so interesting how the statisticians took apart the story. It was amazing how the professor was able to tell which coin flip record was real, because of the unlikely flips. That expirament really revealed the likelihood of crazy events happening in everyday life. People often think that something out of the ordinary will never happen to them, but they can happen to anyone! Although the statistics show that really anything can happen, I like to believe that the Laura girls were meant to meet each other and become friends. Despite the stats, it's nice to believe there is still some magic in life.

May. 17 2014 01:09 AM
Kirby Slater from Long Beach

The fact that out of the however many people in Europe that there are that the balloon just happened to be found by another Laura Buxton. Like what Jenne said, the first idea that pops into my head is 'miracle' because this is one of the things that nobody couldve imagined ever happening, and the probability of this occuring was most likely next to zero. In addition, the odds of a girl with the exact same name with the exact same spelling is within a balloons distance is another thing that is very uncommon. With these odds all stacked against this miracle from happening, Laura Buxton and her balloon found a way to make miracles happen without even realizing how special they were.

May. 16 2014 09:28 AM
Cindy

This radio podcast was very interesting to listen about randomness and probability. I found it surprising that the two girls, alike in name, both had the same pets and styles of clothing. However, if you look at some situations that seem highly improbable in a different perspective, they would seem less impossible. I didn't think that looking at various details other than just the similarities would make a difference in the overall feeling and effect of an uncommon event. For example, flipping seven tails in a row may seem unlikely, but when you flip repetitively for a hundred times, the probability of doing that action is more likely. Nevertheless, some occurrences, such as the red balloon flying to a girl with the same name Laura Buxton and sharing some similar traits, can still remain astonishing to hear. xD

May. 16 2014 04:46 AM
Eason from Irvine

That's amazing! I mean, I didn't know there was something like these can be happen, but that's the truly happened. I think, when a population base is large enough, those small probability events would show up to us. In fact, it's really exist, but because of that probability is too small, so we ignore that event.

May. 16 2014 02:53 AM
Michael Doorly from Southern California

This is a very interesting story because it talks about the possibilities of not probable things happening in real life. What I thought was very interesting was that the balloon flew across the country against the wind. I am not sure if it is a miracle, or chance, or luck, but it is definitely something crazy. Especially because they were around the same age with the exact same name. Also, I thought that it was interesting how they said that it is very unlikely for a person who has won a lottery a first time, to not win it a second time.

May. 16 2014 01:31 AM
Kathern Nguyen

This podcast was really intriguing. The balloon story was crazy though. The probability of the balloon story was extremely low. This podcast taught me how to believe in miracles and how probability is just a gamble. You should always look up to the bright side in life, even though the changes are slim.

May. 16 2014 01:26 AM
Yu from Anaheim

There was a story of Laura Buxton who lives in England. It seems that in June 2001 she released a helium filled balloon during celebrations for her grandparents' gold wedding anniversary in Blurton, Staffordshire, England. Attached to the balloon was her name and address and a note asking the finder to write back. Ten days later she received a reply. The balloon had been found by another Laura Buxton in the garden hedge of her home in Pewsey, Wiltshire, 140 miles away. One Laura was 10 years the other was 9 years 6 months. Both had three year old black Labradors, a guinea pig, and a rabbit. When they met t hey were the same height, had the same hair color, and were dressed in similar outfits, both wearing pink jumpers and jeans. They each had brought, unbeknownst to the other, their guinea pig with them to the meeting. Both guinea pigs were brown and each had an orange patch on their bottom. Each girl had a pet rabbit - a gray one, and a 3-year-old black Labrador .

All people had a very lucky times sometimes, you find a book you lost in long times ago, maybe you are that person who won hundred dollars one times. or you get two free taco in jack in the box. You have chance to get everything, even the probabilities are really low, all the things you need, is a little lucky, lucky means you got something and it is hard to get,but if you tried more times, you have more chance to get it, like the people who bought the lottery tickets, if you bought more numbers, you got more chance to win it, like Buxton, if she released more balloons, more people have more chances to get those balloons, so more tried , more chances, also more probability, that is more lucky.

May. 16 2014 01:24 AM
Madeline Frank from CA

I really enjoyed this story. I thought it was the coolest thing that the balloon just happened to fall into the hands of another Laura Buxton. I personally believe this to be fate to matter what the probablility. The fact that these girls even became friends afterward is incredible. I also thought the experiment with the coins was interesting. After the man explained that it really wasn't that uncommon to get 7 tails in a row the probability of it made much sense to me. I especially liked the quote, "Strange things do happen by chance." This made a lot of sense to me and I think the idea of chance is very interesting. I learned a lot from this broadcast!!!

May. 15 2014 10:52 PM
Mary Wilson from California

I listened to this podcast for my geometry project and it was really interesting to hear about these stories because I never realized all the possibillities that could happen and the probability of these things happening. I learned that things can seem a lot more magical until you hear the entire story with all the details. Like in the Laura Buxton balloon story, they told all the similarities first to make the story seem really impossible, but at the end they told us that one girl wasn't ten years old yet, they liked different things, and someone could have seen the name on the balloon and looked for another Laura Buxton to give it to. After they added in all the details, it showed me that sometimes strange things do happen by chance and the probability is a lot higher when you add in all the details and possibillities.

May. 15 2014 09:01 PM
Jenna Mattson from California

This podcast was very interesting for me to hear. Being Catholic and having faith, when i first heard the story I immediately associated this with a miracle. When listening, I learned you should not associate everything with being a magical happening or miracle. Do not get me wrong, I live for miracles, but I need to focus on not confusing this with chance. In geometry we are learning about the probability of occurring of certain happenings. I liked this podcast because it kept me entertained and wanting to hear the rest of the stories about chance and occurrence. Something i have not thought about until now, is that each one of these acts was bound of happen some day, and it just happened to those two lucky Lauras. Thank you for sharing this Ms. Rushman!

May. 15 2014 08:28 PM
Garrrett

Wow! I think it is crazy how the kite randomly ended up in that certain neighbors house with the same exact name, almost the same exact age. This podcast was very entertaining and definitely not boring, in that I didn't get distracted by anything else. Also the numbers aspect was pretty interesting on how getting 7 tails in a row was not that cool unlike they had though. Overall it was very well put together story.

May. 13 2014 01:07 AM
Alex GArces-Saldana from Southern California

I think this was an absolutely amazing story. I also found it very interesting how the men found all theses statistics that made the story that much more interesting. I personally at the beginning felt as if it was a miracle and I thought to myself, what are the odds? But as the men continued spot speak on the topic of my question I realized that it was bound to happen somewhere and sometime. That it juts happen to be these two girls. The fact that there story about the golf ball landing on a blade of grass made the story a lot less interesting or like it was bound to happen. Even though the chances are so unlikely there is always that one in all the numbers of statistics where this has to happen. And to be that one probably made the girls feel special at the time but to be straight up it was all part of a plan possibly God's plan. In the end I thought a lot less highly of this story yet there was still an aspect that was amazing to me because how often would you here this story. The fact that they decided to tell the story and for it to be on the radio is another part if statistics. Maybe this has happened to someone else but did they tell there story? I don't know because this is the first that I have heard of it. Another part that amazes me is how my teacher told heard the story and then had us listen to it. What are the odds she would happen to listen to it? And then on top of that tell her students about this. It all come together to be a bunch of amazing statistics from the story itself from me myself being able to have someone tell me about it after they happened to listen to it themselves. What is a miracle to me may not be to others but the chances of this are so slim which is what amazes me most.

May. 12 2014 01:51 AM

This radio piece was very intriguing. it helped put a different perspective on the way I look at life and why things happen do happen. Most of the time it is a lesson for your future, just put there by destiny. The world does some amazing things for your life. These things happen for a reason, and this just showed that to me. That no matter what, things happen to affect where you are headed. The world is a wonderful place.

May. 11 2014 09:53 PM
Kate Hampton from Southern California

Strange things do happen by chance. The word chance is a very difficult one to comprehend for it is based on complete randomness. Some things don't just happen for a certain reason and we must all learn to just accept it as it is. One thing that I learned from listening to this show, is that if you don't see past yourself you automatically fall prey to superstition. We have to be careful to not find meaning in a miraculous situation when it is just plain coincidence. Even though I am a true believer in miracles and fate, I now realize that not everything is filled with magic and fantasy. I know, I know--it's hard for me too, but we don't have to call a situation magical just to enjoy the experience. I hope everyone learned a lot from this geometry activity just as much as I did. Thanks Miss Rushman:)

May. 07 2014 09:32 PM
Nick sarmiento from Southern California

This podcast was quite interesting because it opens up you more to thinking about how this world comes together. When I listened to this documentary it got me think on how possible it is; how something inconceivable could possibly happen. In my everyday life I come across things that get mind on thinking how this possibly could have happened in mathematical statics and I find it very interesting. Somethings that were in this podcast that actually got me thinking, were how the numbers were put into these situation that the two men came across. How their experiences lined up with all the statistics can really put the human mind into motion about probability and it did mine.

May. 05 2014 11:58 PM
chad from Atlanta

Thanks so much. I haven't read anything so profound since my logic professor's paper exposing Noam Chomsky.

Apr. 14 2014 10:35 PM
Gene Yakub from Italy

For those who believe in coincidences these types of events, and similar ones which can be placed under "coincidence", seem wondrously unrelated and unexpected. But to those, like myself, who know that reincarnation is a reality, everything happens as it is supposed to, as has been chose by us before each reincarnation.
How can it make sense that as we look around us, there is a continuity and a unity even in diversity that has been there since the year dot, all fits together perfectly, everything sustains everything else - or it did before we interfered.
Yet we humans supposedly live a comparatively brief life span and all our experiences and knowledge disappear into thin air with that body? Why would that be true of the most sophisticated component of all creation?
What is human life about then, what is the purpose of being alive? Just to waffle along and accumulate book knowledge so as to earn money? No, life is for learning and growing, to rid ourselves of the negative consequences of the mistaken choices we previously made (the Law of Action and Reaction, Cause and Effect) by having as many other opportunities as necessary to understand where we went wrong and correct ourselves so we can move on.
Destiny v. Freedome of Choice? No versus, they act in tandem when we have to make choices every single moment of our lives because we don't remember what happened in a previous life except during the transition stage between one life another when we make our choices for the next one.

Dec. 04 2013 01:43 PM
Mike Anderson from Australia

Before we can deny meaning and ascribe everything to randomness, we really ought to ask the question: how do we know that "randomness" itself exists?

Apr. 29 2013 01:09 AM
maryam

enjoyed it as usual!

Apr. 28 2013 08:33 PM
Susan from Sea Cliff, NY

27 April 2013
Very much enjoyed this program, as I ALWAYS do! (Superlative=statistical hyperbole?) …So here I am, thought stimulated, free associations flowing…

Would love to hear this conversation broadened to include input from a rich cross section of thinkers and experts! I am neither mathematician, statistician, nor formal student of philosophy, but I believe that there exists a sense of scale, which is a valid participant in the randomness versus pattern theme. I think this sense is most likely species-specific, based on size and reach --physical and technological/cultural-- of each creature (microbes different from ants different from humans, etc. --Ponder the fly flying around inside an airplane flying across a land mass on a planet rotating and revolving…..etc.). Therefore, within the "human scale" of existence --in an atmosphere of cultural exchange, technological reach, our averaged physicality, and certainly our curiosity and intellect-- certain occurrences are legitimately extraordinary or plain, and in that regard, either random or patterned. …Or, as the feature suggests, possessed of some element of magic or manipulation; being on the spectrum of delight, fascination, or fear which makes up the (as yet) unknown; or predictably controlled. If we must always step back and consider scales of the Universe, Eternity, and Infinity, I think we would have no measurements of anything, since by definition, measurements, or numerics, are always relative…to something within our grasp. A disaster for a culture which has come to so worship "measurables." Am I correct that mathematics is a human construct that begins with us? Ten fingers, ten toes; the span of a stride in "feet," a horse is eighteen "hands" in height; time/distance in the pace (and regularity, or not) of the heartbeat; intervals of sunrise/sunset, climate versus weather within our observation.

I would look forward to explorations between a consortium of perhaps existentialists, statisticians, mathematicians, and astrophysicists. But I would take nothing away from your "programmed" attention, to the myopic assumptions to which we too easily fall victim, as we endeavor to stay ahead of bell curves. Patterns are constantly evolving from seeming randomness, particularly in the big data moment currently pressing us. But they are only meaningful to the extent that we can step back far enough in time and space and whatever other dimensions to perceive and apply them to our existence.

Apr. 27 2013 03:30 PM
jen from ayer, ma

@ mills from Virginia, I just saw this after hearing the thing on the radio about the 2 Laura Buxton's 4/25/13 and coincidences... Anyway my father was born on July 4, 1949 and died when I was little in 1977 and my grandfather, his father died on the same day that his son was born years later on, July 4, 2006. We all thought it was weird but We all think it was strange but comforting somehow that they are both together again.

Apr. 25 2013 10:53 PM
dr

awful audio - the effects are not the least bit surreal or provocative... just bloody annoying

Jan. 04 2013 03:42 PM
WatchTheClock from Up

The balloon story was really interesting, but I couldn't help but think of all of the wildlife destruction that is caused by balloons.
PLEASE don't release a balloon. Balloon releases are "celebrating by littering."
Dolphins, whales, turtles, and many other marine species, as well as terrestrial animals such as cows, dogs, sheep, tortoises, birds and other animals have all been hurt or killed by balloons.
More information here: http://balloonsblow.org/impacts-on-wildlife-and-environment

Jul. 14 2012 02:17 PM
shannon from fraser,Colorado

It is so weird and remarkable.well they do say you do have a twin somewhere!

Mar. 25 2012 10:27 AM
BOB

Hi

May. 23 2011 08:01 PM
Jim

I think they were twins, maybe separated, who made up the story to get popularity...

May. 08 2011 09:49 PM
Jay Koehler from Chicago, IL

Sorry to weigh in so late in the game here, but I just saw this site for the first time today (4/27/11). I'm the "statistician" from this particular Radio Lab show that at least one of you asked to hear from.

Yes, some of you math critics are right to say that the chance of the run in question is about twice as large as my estimate. Nice work. But there was some confusion about what was being computed due to edits (confirmed by the producer) and my own on-the-fly estimates. You can see more computational detail than you ever cared to see at this website which was posted by another listener.

http://www.leancrew.com/all-this/2009/06/stochasticity/

For the quick scoop on where my numbers on the show come from, scroll all the way to the end of the posting where it says "Update 6/20/09." Mystery solved.
- JK

Apr. 28 2011 12:14 AM
Joe from England

A similar occurence of mine was when i ended up talking to a young girl at a music festival over here, in England, a couple of years ago. I was 22, she was 16. I was a very withdrawn kind of person who was too anxiety-filled to engage with people i didn't know and so i would just spend the weekend wandering the festival on my own, occasionally being around the folks i went with (they were much older than me and not that interested in the music, being the reason i wasn't with them much), trying to avoid communication with anybody... *sigh*

Anyway, this one night, this young girl who was camping nearby comes over to our tents, the tiniest bit tipsy, and starts talking with us. She was fully lovely & enjoyable company and because i could tell that straight away i felt ok talking. And we talked.

To cut a long story short, it turned out we both had a mother going through cancer - not the most uncommon thing, this one - but also that she had a brother in New Zealand at the time.... as did i. So you start to think "oh, well, this is a bit weird. Of the 30,000 people at the festival, the one person i end up talking to has these such things in common..... (blah blah blah)".

And it got even weirder and more random to me when i mentoned some place we stopped off at on the drive up. I don't travel a lot. My county and London are the only places i've been, really, in England, other than when we lived further north till i was 4. The festival was about 3 hours north from where i lived and 2 hours south from where she lived which, in England, is almost half the country away.

And when i mentioned this one lovely place we stopped off at on the way up to have a drink and some lunch, she just looked in shock and kinda half-screamed, in disbelief, "Oh My God! I know that place!".... It turned out that this one place was the place her and her family go almost every year for a short holiday and it was just pretty mind-blowing, really, to find that out, along with the other connections we had. And by place, i mean the exact same pub/inn, not just a village, or a town or a county.

So the one person i had spoken to, for many years, of whom i previously didn't know, at a festival of nearly 30,000 people turned out to have a mother with cancer, a brother in New Zealand, and knew greatly the one tiny place i had stopped off at on the way and, other than the festival itself, the one place in nearly 20 years i had been to outside of my home county & London.

It's still very weird, to me.

Feb. 07 2011 07:37 PM
Maxwell P. Blakeney

I LOVE radiolab. Every once in a while I re-listen to an old episode. Today was Stochasticity. I'm really hoping you guys can tell me the name of an song in the episode. It start playing It starts playing at about 27 mins into the show right after Jad says something to the effect of "Essentially what you're saying is that basketball players are like coins." It sounds familiar but I can't seem to place it.

-Hoping you can help me out

Dec. 17 2010 01:24 PM
Truman Buffett from Seattle

This link got posted elsewhere, but not here:

http://heymathman.blogspot.com/

(these videos are now >1yr old.....sorry this link didn't get posted here sooner)

Truman

Nov. 25 2010 01:29 AM
James Plaskett from Cartagena, Spain

Right at the end of the Podcast one of the Lauras says she is studying Engliah, History and Classical Civilisation.

I studied those same three subjects when I was that age!

Uncanny?
Er, no...

But some better coincidences visible here -
www.jamesplaskett.com/

Jun. 30 2010 11:04 AM
Victor Salvest from England

I wish that your statistics prof would weigh in with the answer. My assessment is as follows:
A. there are 2^(100-7) ways for the first tosses 1 thru 7 to come up heads; if the first 7 are heads then the next 93 can be anything we like which can be arrived at in 2^93 ways.
B. if the next 2 thru 8 tosses are all heads AND the 7th toss wasn't a head (to avoid a double count of the run we got in A) there are 2^92 ways for this to occur- (run of 7 with 92 tosses which can be anything and 1 which must be a head). In fact ALL runs of 7 after the first can be done in 2^92 ways, we dont care about the 92 other tosses as long as the toss before our 7 isnt a heads.
C. the number of runs of 7 is thus:
(2^93) + (93 x (2^92)) which equals 4.571 x E^29 in scientific notation
D. the total number of possible sequences of throws is 2^100 which equals 1.26765 x E^30
E. the probability of at least one run of 7 heads in 100 throws is C/D or 37% ... I think?!

Apr. 07 2010 02:32 PM
August Mohr from Boulder Creek, California

Dear Mr. Truman Buffett,

I would like to see your video. I think it was Ross Ashby's book, Cybernetics, that presented Markov chains of English words which read like beat poetry that made the concept stick in my mind.

But I got no results for a Facebook search on your name. Would you please try mine? I'm the only "August Mohr".

Ashby's method was brilliantly easy to do in a searchable document like a PDF. Open a book and copy the 1st word. Search for the next instance of that word and copy the word that follows it. (If the 1st word is unique in the book, loop around to the only word that ever follows it, the 2nd word in the book.)

The 2nd word is a statistically like any words that could follow the 1st word, without the extra "meaning" of being the word that follows in the same sentence (unless it's unique).

Search for the next instance of the 2nd word, copy the following word the 3rd word in your Markov Chain. Keep moving through the text and you can make an arbitrarily long sequence in which each pair of words was generated with the probability of those words being found as a pair in the text.

That string of random words will have lots of "interesting" strings of 3 and 4 words, but no meaning. Unless you want to go into Bible Code land, that is.

What is usually omitted from Bible Code "statistics" is that the old Hebrew texts they use have no spaces and no vowels. Strings of only consonants are much shorter strings to match than most modern words and they may be interpreted as a word or words in multiple ways, thus radically increasing the opportunity for the searching mind to find things that correspond with each other. The human mind puts the meaning into the "random" proximities, like seeing Jesus in the spots on a Holstein cow.

What statistical analysis leaves out, is that once a mind has added meaning, there is meaning there. Nothing in the world has any meaning except that which has meaning to someone.

Mar. 09 2010 04:52 AM
Gina Mireault from Vermont

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!

Nov. 22 2009 09:21 PM
Truman Buffett from Seattle, WA

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.

Nov. 17 2009 10:00 PM
Yanming from Corvallis

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.

Nov. 17 2009 02:49 AM
Truman Buffett from Seattle, WA

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.

Nov. 14 2009 03:53 AM
Terry Hayes from Lexington, Ky.

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.

Oct. 10 2009 01:37 PM
Irene Cardenas from Minneapolis, MN

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.

Oct. 05 2009 04:15 PM
EERac from New York, NY

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.

Oct. 05 2009 03:41 PM
Mills from Virginia, USA

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.

Sep. 22 2009 09:34 AM
Michael Shulman

@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

Sep. 12 2009 01:42 AM
Alan

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.)

Sep. 05 2009 05:29 PM
Chris

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.

Aug. 11 2009 03:14 PM

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