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The Problem With Probability

Blinko_Glick

Blinko_Glick

Gone But Not Forgotten
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If you've ever read Douglas Adams' Meaning Of Liff, you may, like me have given an obscure place name to an everyday event or 'thing' which doesn't already have a name.

I have one. It's a Heavitree.

A Heavitree is when you open a packet of tablets and you inadvertantly open the end where the instruction leaflet is wrapped around the pill trays. You can't easily get the pills out, so you have to open the other end.

A small annoyance surely?

Well yes, if the laws of probability worked properly, you'd expect a 50/50 chance of encountering a Heavitree.

But what if you took daily tablets and every day for the last several months apart from 3 times, you get one?

Well this happens to me. Am I just unlucky?

I've become so exasperated by this that I now leave the packet open at the right end so that the Heavitree cannot mock me any longer.

Has anyone else noticed something that seems to defy the laws of probability?
 
Having just examined my pill packets (which can all be opened from either end), and exercised the little grey cells, I come up with these ideas:

Presumably all pills are machine packed and so are identical. Therefore the explanation must lie with the user. I suggest that it might depend on whether you are right-or left-handed. It could be that most right-handers hold the pack in their left-hand and open it with their right, and vice-versa for the lefties.

There could be further subdivisions - do people pick up the pack with the printed name on top, or with their chemist's label on top? If the latter, are chemists consistent in the way they apply their own sticky labels? (They ought to be - if the chemist's label says 'Aspirin' but the box says 'Cyanide', it would be a useful safety check to insist that the box is the right way up before applying the label!)

There is another factor to take into account - all my packets have a distinctive printed bar at the RH end, giving the size of the individual pills (eg, 5 mg, 10mg, 500 mg, etc). Does this bar influence users choice on where to open the packet?

So, plenty to think about there - enough for a research project, I would think! (The things I do for science...! :roll: )


But one final thought: medicine and pills are big, big business, so it is highly likely that this research has been done already!

So if most users experience a 'Heavitree', it's because TPTB want us to! :shock:

Why should this be? The obvious answer would be, to maximise the chance that new users of any particular pill do find the info leaflet before they start popping the pills. (Of course, this doesn't ensure that they will read it, or even that they can read, or that they can understand what they do read anyway...!)

Meantime, we hardened, long-term pill poppers just have to get used to popping the leaflet straight into the paper-recycling bin... :D


I'm especially interested in pills this week, having made a unilateral decision to stop taking one of my meds because I don't like one particular side effect. But it will be interesting too to see if this helps with another problem I've been having...

Most leaflets list so many possible side-effects that I'm beginning to think that most of us would be better off without any pills at all.

Of course, the big pharmaceutical manufacturers do not want this message getting out, so

PLEASE COPY THIS POST AND EMAIL IT TO EVERYONE YOU KNOW BEFORE THE HIT SQUADS COME IN AND TAKE DOWN THIS MB (again.. :roll: ) AND ELIMINATE YOUR HUMBLE CORRESPONDENT

- rynner

PS: Why a 'Heavitree'? :?
 
Gosh - good reply Rynner! Thanks.

Heavitree is an area of Exeter. The name always struck me as a bit odd, so when I decided to name this pill leaflet event, I chose the oddest place name I currently knew well.
 
Blinko_Glick said:
Gosh - good reply Rynner! Thanks.

Heavitree is an area of Exeter. The name always struck me as a bit odd, so when I decided to name this pill leaflet event, I chose the oddest place name I currently knew well.
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I recognised the place-name, having whiled away some of the best years of my life in the fair city of Exeter... :D

While (ahem) researching this topic, I noticed that the pills I've decided to stop taking are manufactured in Barnstaple, which is also in Devon, and coincidentally (or not) is where my daughter was born. And coincidentally (or not) she gave birth to a daughter herself, just last week...

Funny old world! 8)
 
rynner2 said:
While (ahem) researching this topic, I noticed that the pills I've decided to stop taking are manufactured in Barnstaple, which is also in Devon, and coincidentally (or not) is where my daughter was born. And coincidentally (or not) she gave birth to a daughter herself, just last week...

Funny old world! 8)
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And I bet she did it without the help of an instruction leaflet. :)
 
And this girl - what are the chances of this, eh?

Schoolgirl goalkeeper scores twice from her own penalty box
Emily Dickson, a schoolgirl goalkeeper, is thought to have broken a Football Association record after scoring twice in a single match from her own penalty box.
By Murray Wardrop
Published: 7:00AM BST 19 May 2009

Emily, 14, stunned her team-mates and the opposition when she launched two huge drop kicks more than 100m down the full-sized pitch.

With both attempts, the ball bounced over the opposing keeper and into the net during the under-15s match. :shock:

Emily, from Broxbourne, Herts, is now awaiting confirmation from officials, who believe that her effort is an FA record.

The Hoddesdon Owls Girls player said: "I'd never scored a goal from my goal before. So it was totally brilliant to get two in one match." :D

By scoring two goals, Emily, a pupil at Broxbourne School, helped her side to defeat the Stevenage Vixens 3-2.

The FA's official historian David Barber believes that Emily, could be the first keeper in the country to have scored twice on a full-sized pitch in a competitive match.

Mr Barber said: "Twice in a game I've never heard of at any level."

Emily said that her first goal came after she angrily kicked the ball as hard as she could after conceding a goal.

Emily, who has been playing since she was eight, said: "I was in a really bad mood because I'd just let in a goal.

"I took the ball and smashed it as hard as I could when it came to me. It bounced over the keeper and went in. I couldn't believe it."

She added that her manager came onto the pitch afterwards and told her "double or quits", priming her for a second attempt.

Emily said: "So when the ball came to me next, everyone shouted 'shoot', so I did and in it bounced." :D

Mr Barber added around a dozen professional goalies in Britain have managed the feat once in a game – notably Pat Jennings, Peter Shilton, Steve Sherwood and Steve Ogrizovic.

Emily and her family are avid Fulham supporters and she took up the sport with the encouragement of her two brothers – her twin Henry, 14, and Jamie, 17.

Although Emily is in line for an FA record, she is still one goal away from the world title.

The Guinness record for most goals scored by a goalkeeper in one game is three, and was achieved by José Luis Chilavert of Paraguay for the club Velez Sarsfield in their 6-1 defeat of Ferro Carril Oeste in the Argentine Primera Division, on November 28, 1999.

http://www.telegraph.co.uk/news/newstop ... y-box.html
 
Back to the tablet box. It has happened so often [actually every time for the past few years as I can't remember ever opening it at the right end] that I wondered about the probability myself.
It is a mild but existend annoyance as I believe to be a moron every time it happens.
Reading your account, I first thought along the lines of Rynner's reasoning. Maybe because we read from right to left and pick the box up, inadvertently opening the bottom side. However, I sometimes don't even look at the packet, just grab it and open whatever side comes naturally and darn it is always the wrong one.

Just this morning I was thinking about it again as I started a new packet and as far as synchronicity goes, here we have it.

;)
 
Every time I open a new packet of pills, without fail I get the leaflet end, but every time after that until I finish the box, I get the other end. I don't know what this means in relation to Heavitree, though.
 
Yeah I have the same problem, and I too have been pondering it! I take three types of tablets a month.
One type has only one opening end, which is opposite to the leaflet so its 'wrong' by default (that scuppers one theory).
The other two types have only been undone at the 'convenient' end only once in two years.

The big difference is that for me the wrong way is to have the leaflet at the unopened end, as it interferes with putting the tabs strip back in the carton. I prefer to open at the leaflet which I can then rip out.
 
rynner2 said:
So, plenty to think about there - enough for a research project, I would think! (The things I do for science...! :roll: )...
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There's maybe another factor.

Anyone who regularly has to shift heavy weights around will tell you that the safest and most efficient way to carry an object of non-uniform weight distribution is with the heaviest end at the bottom.

I'm fortunate enough to have little experience of pill packets (yes, I know, my time will come) but I assume the end with the leaflet in is the lighter end - being both made of lighter material by volume, and also forcing the heavier stuff to the other end of the box. I wonder, albeit that it's a relatively small weight we are talking about, whether our hands, sensitive tools that they are, automatically pick up an object 'weight-down' and therefore leaflet-up.

(Plus. Why is it that, the interest that problems like this involve increases in proportion to the amount of important stuff you actually have to do in a day?)

edit - I've just realised that maybe most pills are blister-packed and therefore my observation is not only based on wrong information, but also just plain wrong, as the end with the paper in will actually be the heaviest end, the rest of the weight being evenly distributed.

Bollocks!

edit (again) - Coincidentally, I'm at the moment reading Leonard Mlodinow's, The Drunkard's Walk - How Randomness Rules Our Lives. Maths is not a subject that comes naturally to me, but this is extremely readable and quite funny - it's also full of historical details and anecdotes, which somehow makes the subject a lot easier to absorb. To quote one of the Amazon reviewers - 'Abstract notions are never allowed to wander far before being pinned down by concrete illustrations, often taken from remarkably current affairs' - which is why it works for me.
 
I'd go for the left-handed/right-handed theory with the pill packet.

I can't speak for everyone, but if I need a paracetamol, I'll naturally pick up the packet with the front facing me, and then open the right-hand side of the box. Depending on the brand of medicine, I either almost never or nearly always get the leaflet end.
 
The odd thing is that I never looked at the packets when I picked them up, just left it to chance as to which end I would open - I always thought 'I bet I bloody get a Heavitree again' and lo & behold I would.

However from this point on I shall, upon opening a new packet of pills and encountering a Heavitree, rip out the aforementioned leaflet and bin it.
Thereby negating any further chance of Heavitreeness. ;)
 
Blinko_Glick said:
...from this point on I shall, upon opening a new packet of pills and encountering a Heavitree, rip out the aforementioned leaflet and bin it.
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Or you could read the leaflet, take fright at all the side-effects, and bin the pills instead!

:D
 
'Fraid the withdrawal symptoms are worse than the side effects, and given the current state of affairs in the BG household, giving up SSRIs would be like walking around with a sword of damocles on a sky hook above me. :?

Interestingly, on the packet of sleeping pills I bought the other day, it had the caption: "May cause drowsiness".

I should bloody hope so too!! :D
 
An answer is at hand, given to me by someone who handles pill-boxes for a living.

Look at a brand-named box of tablets (doesn't work with the plain, white boxes used by pharmacists.) At one end there's the brand name, drug name, and dosage. At the other end, the embossed batch number and expiry. The leaflet is always folded around at the batch and expiry end.

All you have to do is open it at the brand name end.

[Alexander the Meerkat] Simples![/Alexander the Meerkat]
 
Cool - thanks Stu.

Only problem is, i never consciously looked at the packs, so i have to believe that ;

a. Probability has gone and turned a bit squiffy

or

b. I have been subconsciously opening the packs in the same way every time.

Neither strikes me as very plausible, but out of the two, b. sounds best using O's R.

Secretly though i'd love to be emitting a probabilty field to affect outcomes. But it be nice to be able to control it. ;)
 
If that system really worked, I'd have thought the professor would be very rich by now. :roll:
 
Ronson8 said:
If that system really worked, I'd have thought the professor would be very rich by now. :roll:
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Clearly, you didn't read (or properly understand) the article, which actually emphasises what low probabilities there are for any particular outcome.

In the long term, betting on many matches using these probabilties, you'd expect to come out about even!
 
I'm dusting off this old thread to ask a question and maybe start a few arguments. My question is this:

What is the probability of someone correctly calling 10 coin tosses in a row? Is it just 1 in 2 or is it some huge number? I do not know that answer and hope someone with a far better grasp of probability can let me know.

So to be extra clear: I hold the coin. The other person calls Heads or Tails. I flip it and they are right. We repeat this process 10 times, them calling Heads or Tails as they see fit. What are the chances that they will be correct 10 times in a row?
 
I'd say still fundamentally 1 in 2.

Each toss event is independant of the preceding one...we might perceive an additional sequential linkage (in terms of a rhetorical "what are the odds?")

Or what am I missing?
 
The answer is 1 in 2^10, ie, 1 in 1024.

(You need to multiply together the probabilities for each toss.)
 
Blinko_Glick said:
Gosh - good reply Rynner! Thanks.

Heavitree is an area of Exeter. The name always struck me as a bit odd, so when I decided to name this pill leaflet event, I chose the oddest place name I currently knew well.
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Douglas Adams spent a fair while with his family in our neck of the woods whilst writing HHGTTG, with the result that several local villages have become immortalised as monikers for slightly unpleasant phenomena. His sister still lives here :)

from http://www.bournemouthecho.co.uk/ne...hikers____Guide_author___s_other_finest_hour/ :

"Douglas Adams and John Lloyd cut an amusing swathe through Dorset. Here are a few of their originals: Bishop’s Caundle: An opening gambit before a game of chess whereby the missing pieces are replaced by small ornaments from the mantelpiece.


Dorchester (n): A throaty cough by someone else so timed as to obscure the crucial part of the rather amusing remark you’ve just made.


Henstridge: The dried yellow substance found between the prongs of forks in restaurants.


Kimmeridge: The light breeze which blows through your armpit hair when you are stretched out sunbathing.


Tincleton: A man who amuses himself in your lavatory by pulling the chain in midpee and then seeing if he can finish before the flush does."
 
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Ermintrude said:
I'd say still fundamentally 1 in 2.

Each toss event is independant of the preceding one...we might perceive an additional sequential linkage (in terms of a rhetorical "what are the odds?")

Or what am I missing?
Click to expand...
rynner2 said:
The answer is 1 in 2^10, ie, 1 in 1024.

(You need to multiply together the probabilities for each toss.)
Click to expand...

AHA! Two sides of the same coin (do you see what I did there?) Each coin toss, is in itself, a 1 in 2 chance. And each sequential toss is still a 1 in 2 chance. BUT, as Rynner suggests, I think that as a series, each call being correct, after 10 attempts, the odds of each call being correct would be 1 in 2 to the power of 10 (1 in 1024).

Right?
 
Ringo said:
AHA! Two sides of the same coin (do you see what I did there?) Each coin toss, is in itself, a 1 in 2 chance. And each sequential toss is still a 1 in 2 chance. BUT, as Rynner suggests, I think that as a series, each call being correct, after 10 attempts, the odds of each call being correct would be 1 in 2 to the power of 10 (1 in 1024).

Right?
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Correct.

However, for every toss in isolation the chances are still 1:2. So thinking that if you (say) toss 6 tails in a row, you are 'due' a head, is the 'gambler's fallacy'.
 
I have only ever been called on to deliver simple lessons on classic probability theory but mathematicians delight in some paradoxical examples which seem to throw it into doubt.

We know that the standard method seems to come a cropper with the Monty Hall Problem, previously discussed. The Wikipedia page has quite a good graphic which helps to clarify the problem and maybe the causes of confusion.

There are other classic cases. The Bertrand Paradox, for example.

The geometry required to understand the problem is very basic. Try the first two methods, which seem equally logical but which deliver odds of 1 in 3 and 1 in 2 respectively! :evil:
 
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