What has a 1 in a million chance? (2010)
stat.berkeley.edu
stat.berkeley.edu
-- Terry Pratchett
Making fun of the fact that if someone says "it's a million-to-one chance, but it might just work!" in fiction, you know it's going to work.
In _Guards! Guards!_ this is taken to the point that they reckon that it's not enough to hit the dragon with the arrow at the soft spot, they also have to try a whole bunch of improbable circumstances to get the chance to exactly 1 in a million. Because exactly 1 in a million is hard to achieve, as the article shows.
I can't find the wiki link, but Ronald O'Sullivan, who'd just taken over his father's cheese shop, was attempting to make a single block of swiss after a long week of selling the first 80% of several blocks to different restaurants. He took those cheese tails and stacked them up, not realizing the dangers he was putting everyone else in. It was later found that there were several other contributing factors; he hadn't used a properly certified cheese cutting blade (baloney!) and had reused the wax liner to store the off-cuts prior to reassembling the cheese that ultimately failed.
Some say you can still smell the swiss on hot august days.
"The event entered local folklore and residents reported for decades afterwards that the area still smelled of molasses on hot summer days."
Fondue is a colloidal suspension of cheese solids in a mixture of wine and melting agents and it shows complex rheological behavior. Unlike Newtonian fluids, where viscosity remains constant regardless of the applied shear rate, fondue demonstrates non-Newtonian features, especially shear-thinning. As the shear rate increases, its viscosity decreases, a phenomenon attributed to the alignment of colloidal particles in the direction of flow, interfering with the fluid and preventing it from filling every nook and cranny like a flood would.
Fondue's inability to achieve truly laminar flow is rooted in its viscoelastic properties. When subjected to stress, fondue exhibits both viscous and elastic characteristics, a behavior modeled by the Maxwell model in rheology. This model combines a viscous damper and an elastic spring to describe the material's response to applied stress. As fondue is subjected to shear stress, its structure becomes disrupted, leading to a breakdown in its ability to maintain a cohesive flow front. This disruption manifests as a turbulent flow, preventing the formation of a flood-like scenario similar to that caused by molasses.
I want to congratulate you on writing the most pedantic thing I've ever read in my life. Truly a masterpiece. I can't wait to bust this out in my next aviation related discussion.
If you take a series of unit squares and from each one remove a random circle (ah, the origin of every protracted probability argument among mathematicians: a random circle selected from which distribution?), then stack them up… after n squares, what is the expected hole size? Or how many squares do you need to stack to reduce the hole size to below a particular threshold?
Circle intersection geometry is hard though. Probably easier to start with axis aligned square holes, which are what you get when you make your Swiss cheese out of milk from spherical cows.
https://www.npr.org/2004/02/24/1697475/the-not-so-random-coi...
With a bit of training you can feel the coin with your thumb when catching it to make sure you present the desired side. If you do it quickly enough people won't see you do it. The trick requires coins that have sides that feel distinctive.
«One time, someone asked me what my name was. I said, “Mark Xu.” Afterward, they probably believed my name was “Mark Xu.” I’m guessing they would have happily accepted a bet at 20:1 odds that my driver’s license would say “Mark Xu” on it.
The prior odds that someone’s name is “Mark Xu” are generously 1:1,000,000. Posterior odds of 20:1 implies that the odds ratio of me saying “Mark Xu” is 20,000,000:1, or roughly 24 bits of evidence. That’s a lot of evidence.»
«Extraordinary claims require extraordinary evidence, but extraordinary evidence might be more common than you think.»
The most well known application of this is teaching kids to ask a random shopkeeper for help if they get lost, but to not get in a stranger's car when offered a lift.
(Guys and Dolls)
If an attractive lady walks up to me at a party, first thing I'm doing is asking for references.
The question is are you using the name on your drivers license, which is probably the one on your birth certificate.
> 20 coin tosses (by me) all coming up Tails. YES
> If you tossed the coins then the first answer would be NO, unless I'm very confident you lack the ability to fool me …
Using the same argument I would accept infinite odds that my username is quickthrower2 so there is infinite information?
Gaining a Shannon entropy bit means learning the answer to a yes-no question that had 1:1 odds.
Gaining a log-odds evidence bit means doubling your best-guess odds on a question you are uncertain about, from X:Y to (2X):Y.
One Shannon bit is worth arbitrarily many evidence bits, because a Shannon bit takes you from 1:1 odds to UNBOUNDEDLYHUGE:1 odds. So... yeah, actually, reading your username is worth infinite bits of log-odds evidence on what your username is! (Ignoring practical issues like the small chance of computer malfunctions, of course.)
And to answer your initial question: the 20 just came from the assertion they'd bet 20:1. That was arbitrary.
Going from 1:4 to 1:2 means that the event has become twice as likely. But going from 2:1 to 4:1 does not: it means that the complementary event has become half as likely.
Based on this, we can't do math with odds treating them identically to ratios.
If you do the math correctly, the two types of information measure are basically the same thing.
In the original comment, the evidence update was stated as going from 20:1 to 1:1000000 and it was claimed this was approximately 24 bits of evidence. The update is from 2^4.3:1 to 2^-19.9:1. Subtracting the exponents you get 4.3 - -19.9 = 24.2 which is approximately 24 as claimed. The "20" in 20:1 is correctly accounted for by the ~4 additional bits of evidence on top of updating from 1:1000000 to 1:1.
Clearly evidence bits behave very differently from entropy bits. Acquiring a single entropy bit is an update from 1:1 to 0:1 which is 2^0:1 to 2^-infinity:1. It's worth an unbounded number of evidence bits. It's important not to mix these two things up.
Or perhaps you can provide a reference to a justification of this type of calculation?
I think you're just wrong about needing everything to be in the form X:1 or 1:X. When I compute the ratio of 1000000:1 divided by 1:20 it gives 1000000:(1/20) then scaling both sides by the same factor gives 20000000:1.
I would be very surprised if you can find any reference at all to the number you describe as 'evidence bits', or anything equivalent, made by anyone who can show an understanding of basic probability, statistics, or information theory.
I understand how you get 20,000,000 as the answer to the calculation you carry out. My point is that that number is not meaningful in any way.
For example, suppose you are trying to estimate how much rounding errors in a pseudo random number generator betray that it is not a true exact representation of the random process. One way to quantify this is to compute the expected bits of evidence revealed per call to the RNG.
Mark is a very common first name. Xu is a Chinese surname shared by over ten million people (according to Wikipedia). It’s entirely ordinary that someone would have this combination of names.
Analogy: someone has a winning lottery ticket. Is it the one in your hand? Probably not.
If somebody claims they are holding a winning lottery ticket and will sell it to me for a 50% discount because they are leaving the country in two hours and don’t have time to cash it out, that’s an extraordinary claim and I would need extraordinary evidence to take the deal.
If someone says their name is Mark Wu, it’s like saying they are holding a non-winning lottery ticket with serial number 12345654321. It’s at best a curiosity.
Mark: "I've thought of a number between one and a billion and written it down. The number I wrote down was 6,822,172"
Recursing (you): "ok"
Mark: "ohh you believe me? Then let's take a bet, if I did write down 6,822,172 then you win. If I wrote down any other number between one and a billion then I win".
Would you take that bet? I think you'd be suspicious.
Mark: "I predict that Recursing would take that bet, happily, because why wouldn't they believe me? Therefore them taking the bet is very strong evidence that I actually did write down 6,822,172".
You can't use your prediction about someone else's behaviour as evidence!
Travelling 6 miles (9.7 km) by motorcycle
Travelling 17 miles (27 km) by walking
Travelling 20 miles (32 km) by bicycle
Travelling 230 miles (370 km) by car
Travelling 1,000 miles (1,600 km) by jet
Travelling 6,000 miles (9,656 km) by train
But switching from car to bicycle for short trips still increases life expectancy due to health effects.
Sources: https://en.wikipedia.org/wiki/Micromort https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2920084/
Same with planes. Like yeah if you wanted to make the same trip without a plane it's way more dangerous but what if you just wouldn't take the train from coast to coast in the first place?
IDK, imo time is the most important tradeoff for transport when doing per capital/etc measurements
So in the article about 200 miles driving (in California) is 1 in a million chance of dying. So lets use that number nationwide to be lazy.
Now we can move a decimal point over. So the death chances of a Chicago to LA drive is 100,000 in one. But you drive back, so then its that twice. Once in 50,000 people dying on a Chicago to LA and back roadtrip is extremely frightening. How many people from the midwest make this drive a year? Or from the east coast? How many don't make it back?
The USA, on average, has 100+ fatalities via auto transportation a day.
The above ignores serious injury, permanent disability, etc. Its just death. The chances of having to deal with a broken spine, losing a limb, blindness, 3rd degree burns all over your body, etc aren't even calculated, but those are real and far more common than death. Death being harder to achieve with modern medical treatments.
Cars are extremely dangerous. We downplay what it means to drive.
I wondered about that reading some of the comments about the 737 Max. We routinely travel in exponentially more risky ways all the time, yet we expend time thinking about the safety benefit of avoiding a specific type of aircraft.
Not downplaying airline safety as a whole there, but thinking about it for yourself on a personal level is maybe not moving the needle.
A wave hit it?
A wave hit the ship.
Is that unusual?
Oh yeah, at sea? Chance in a million!
https://www.flinnsci.com/becker-bottle-one-in-a-million/ap45...
The Eurocode defines 3 consequence classes: CC1, CC2 and CC3. CC1 has the lowest consequence and is used for regular homes, light industry and agriculture. The chance of dying as a result of structural failure is low, 0.001. The chance for a CC2 building (apartment buildings, offices, hotels etc.) is defined as moderate with 0.03. And CC3 is for special buildings, such as large stadiums, with a high risk of death on structural failure, 0.3. There are other factors that go in defining a consequence class however, including economic and social concerns.
The consequence class maps to the chance that we find it acceptable for a building to collapse in a given year. Causes can be anything, like extreme weather. For CC1 this is 1 in 100, for CC2 1 in 10.000, for CC3 a chance of 1 in 100.000.
So the chance one or more people die in a stadium during a heavy storm due to structural failure could be 1 in 300.000 in a year if you purely look at the statistics behind the structural safety standard.
The statistics map to simple reference values for the loads of wind, snow, rain, usage etc. and easy safety factors. For example CC2 has a safety factor of 1,5 over all variable loads.
Does this mean 3% or 0.03%?
30% for a CC3 seemed high to me initially (hence wondering if 0.3 really meant 0.3%). But since it actually means "in 30% of structural failures in CC3 buildings (e.g. a stadium), at least one person dies", it make much more sense because there are probably lots of people in the stadium.
> Q > What has a 1 in a million chance
What I found interesting was how often edge cases would occur with that much traffic
Something that would be really difficult to reproduce locally would happen like 100 times a week if you looked at the logs
`from tasuki import random`
But it is a bit of a tricky question. Because you can get hit by a small space rock, it has already happened but it is extremely rare, much less than 1 in a million, and I don't know if there is a record of anyone dying from it. But there is also a small chance of a massive impact killing billions in our lifetime, and intermediate scale events like if the Tunguska event happened in a populated area.
A simple statistical test would give you an idea. With 10B people on Earth, a "one in a million per lifetime chance" would happen to 10M people during their lifetimes. If we optimistically assume that a lifetime is 100 years, and the chances do not change with age, the event would affect 100k people every year.
Then the "one in a million per lifetime" chance would be an event that happens to about a hundred people every year, on average.
Winning a big lottery is within the right ballpark. Flying to space is definitely more rare.
HN comments: https://news.ycombinator.com/item?id=5145268
The chances of dying in a traffic accident in US are between 0.9 and 1.2%, whereas the mortality rate of US military servicemen in Afghanistan has been below 0.004%.
That's 3 order of magnitudes.
Now if during the entire, exhausting, 20 hours of driving, you press a button, and it falls within the "danger zone" that lasts 15 seconds, you lose.
The above example is better when looking at lottery winning chances (worse than 1 in million) - where you can imagine having to throw a quarter out of the window, hoping for it to land within the proper 1 inch section of the road.
I like this example because it gives you visceral feeling - allowing you to think in terms of lengths of road or length of time to compare various odds.
Any reason you chose those numbers? Trying to understand the significance of those odds.
I wanted something around 1:1million odds
This idea also helps to illustrate something which is intuitive to me but seemingly hard to explain. Sometimes when an event occurs people will exclaim, "Wow, what are the odds of that?!" and then if it turns out to be a seemingly unlikely event, then it becomes "wow, it's crazy that happened!".
But it's really not. Using the pull-quote as an example, it's the difference between 1) throwing the quarter out the window and drawing a circle around where it lands and 2) drawing a circle on the ground, hoping to land the quarter in it when it's thrown. Of course the exact result in the first case was unlikely but nobody predicted it so it's uninteresting.
https://jeffgarretson.blog/2014/07/17/one-in-a-million-is-ne...
Worth a read if you are an SRE.
“Hundreds of children die every year in drowning accidents,” he says. “We need lifeguards at pools more than armed guards at schools.”
https://www.city-journal.org/article/sorrow-and-precaution-n...
https://news.gallup.com/poll/266681/nearly-half-fear-victim-...
"Micromort" is a unit of risk defined as a one-in-a-million chance of death, […] used to measure the riskiness of various day-to-day activities.
And apparently a man is about equally likely to die from breast cancer as he is from testicular cancer: both have a lifetime chance of about 1 in 5000.
[1] https://www.cancer.org/cancer/types/testicular-cancer/about/...
In practice, a precise clock and a few difficult to guess events like keyboard and mouse inputs are enough to get a descent seed.
You can only proclaim that something is "truly random" on epistemological grounds, assuming that true randomness is somehow exposed by the universe. This holds under quantum physics, but not under classical mechanics. Unless there is some quantum effect, RNGs based on fluid dynamics, like lava lamps, may be completely deterministic, we just don't know how to set their initial conditions precisely enough.to reproduce a phase trajectory.
But the presence or absence of such a function for a naturally occurring process is, again, an epistemological question. That is, whether we can reverse-engineer the universe deeply enough. Unless we find its source code, we're stuck with retrofitting some formulas, and a "random process" is such for which we can't retrofit any better description than a statistical one.
Only if the person isn't aware of the issues involved.
As you can see, my account is not new. I thought the comment will be funny. Not every comment should be terribly ingenious, long thought and crafted to show people how smart the commenter is. As a commenter you have the right to be spontaneous.
Yeah I did find it funny, no doubt. Was just asking of general culture here
Therefore if a human picks a number between 1 and 1 million, there's only a 1 in a million chance that the number was picked randomly.
https://news.ycombinator.com/item?id=10693664
From 2015, so the style might have changed
but people say things like "1 in a million" because it sounds incalculably rare, so I'm not sure I understand the goal here? to make an exaggeration sit on an intuitive scale as if it was meant literally? if successful that will make being "literally one in a million" fall out of favor just as literally has.
one thing I took away from modestly extensive study of linguistics was, people need to stop thinking that words have strict definitions, and realize that words adopt definitions to suit what people are trying to say. What did they mean is more important than what did they say.
Struck by a Meteorite: The odds of a person being struck by a meteorite are estimated to be about one in 1.6 million.
I wonder how plausible things like this seem to people…
Mary: "I'd say.. more like one out of a million." Lloyd: (slowly reacts) "So you're telling me there's a chance? … yeah!!"
Dumb and Dumber (1994)
reminds me of https://xkcd.com/795/
ELEVEN members of a railway maintenance crew had to be taken to hospital on Saturday after lightning struck train tracks they were working on in WA’s Goldfields-Esperance region.
Winning ~3-4 times at the roulette when betting on numbers?
Being Born on February 29th. NO
Wikipedia has GP's at 649739, so yeah 'almost' a million, roughly speaking. 4 / ((52 nCr 5) - (4 nCr 1)). (Four suits, one way to do it in each suit, deck of 52, five card hand.)
I can't think of any common form of poker where it would be ~6000:1
This sentence desperately needs parentheses. Took me five minutes to parse correctly.
> If we guess a President will serve on average about 6 years, then [1 in (6 times 4.0 million =) 24 million] babies will someday be President.
Switzerland does have a committee of 7 people as president, only a small step from that to 24 million babies.
The more I think about this, the funnier and more complicated this gets.
It can also be done months faster getting multiple humans though.
It’s probably impossible for a population to average that rate though.
Takes about 9 months to output N humans where N approaches to 1 on large averages as even twin births are like 1.2 percent.
Also many females cannot be pregnant again for a while after giving birth, even if we had sped up the pregnancy.
To average 6 babies, we need something like giving birth to triplets every 5 months in average, which improbable even if we had the technology, will and the economics that could support this.
But you know, "improbable" is such a funny word, especially out of context :)
> It's true, if you're on you deathbed and you've only eaten one spider seven more come along and jump right in there at that last second.
I figured it was that sort of reasoning that got us to 24 million babies.