Frederick The Monk

26046. Thu Oct 06, 2005 2:56 am 


I'd just like to add that I too studied probability at A level and have also forgotten how to calculate them.
Must have been the way we were taught. 




Flash

26047. Thu Oct 06, 2005 2:59 am 


Probably. 




Flash

26053. Thu Oct 06, 2005 4:03 am 


I haven't done the test so I don't know how this particular scoring system works, but probability theory is routinely abused by people with an axe to grind in this area. If you toss a coin 10 times you might regard the single most likely outcome as 5 heads and 5 tails, but actually a 6:4 split is more likely, so long as you don't specify which way it's split (ie whether it's 4H:6T or 4T:6H). (There are 1024 possible outcomes, of which 252 result in a 50/50 split and 420 in a 60/40). So, on one intuitive interpretation, the 'aberrant' result is much more likely than the expected one. 




Gray

26055. Thu Oct 06, 2005 4:46 am 


[quote=Flash]If you toss a coin 10 times you might regard the single most likely outcome as 5 heads and 5 tails, but actually a 6:4 split is more likely, so long as you don't specify which way it's split (ie whether it's 4H:6T or 4T:6H).[/quote]
How do you get this result? Any run of heads and tails is equally as likely as any other.
TTHTHHHTTH (10 successive outcomes)
is exactly as likely as
HHHHHHHHHH (10 other successive outcomes)
The probability of either of these (and any other pattern of 10) is (1/2) ^ 10 = 1:1024.
This seems highly unintuitive, but it's true. But all it means is that if you tossed a coin for years, then on average, you would only get exactly the particular run of ten you've predicted every 1024 attempts or so.
1 2 3 4 5 6 coming up in the lottery is exactly as likely as any other combination of six numbers. There are, of course, a very large number of combinations that can come up (around 13 million for 49 separate numbers) and this is just one of those. 




Flash

26058. Thu Oct 06, 2005 5:00 am 


Exactly. There's only one possible version of the 'all heads' outcome: HHHHHHHHHH. But there are:
10 possible versions of the '9 heads, 1 tails" outcome: HHHHHHHHHT, HHHHHHHHTH, etc,
45 possible versions of the '8 heads, 2 tails' outcome,
120 possible versions of the '7 heads, 3 tails' outcome,
210 possible versions of the '6 heads, 4 tails' outcome
252 possible versions of the '5 heads, 5 tails' outcome
and so on, down the other side of the Pascal's triangle until you get 1 possible version of the 'all tails' outcome  TTTTTTTTTT.
Each of these 'versions' is equally likely, but each of the 'outcomes' isn't, because there are more ways to achieve the outcomes in the middle area of the Gaussian distribution curve than the ones at the edges. 




Flash

26062. Thu Oct 06, 2005 5:09 am 


To use easier numbers, if you toss a coin three times, there are eight possibilities:
HHH
HHT
HTH
THH
TTH
THT
HTT
TTT
So in this case the chance of a 2:1 split (as long as you don't care which way round it is) is 6/8 = .75, whereas the chance of the only other possibility (all the same) is 2/8 = .25 




Gray

26067. Thu Oct 06, 2005 5:31 am 


Ah, okay  the precise meaning of the word 'outcome' has confused us here.
By outcome, I had considered specific sequences of results, but you had considered only totals of heads and tails over a number of tosses. It's the difference between combinatorics and permutations, I seem to remember... 




Flash

26069. Thu Oct 06, 2005 5:40 am 


Yes. Where larger numbers are concerned, the result is that the single outcome which is most likely is, nevertheless, very unlikely overall. If you toss a coin a million times, the chance of it coming up exactly 500,000 times heads is very small, even though a 50/50 split is the single most likely result. 




Flash

26072. Thu Oct 06, 2005 6:02 am 


Post deleted 




JumpingJack

26321. Fri Oct 07, 2005 9:07 pm 


Those of you gifted in telepathy, precognition and clairvoyance will have intuited that this thread has been taken over by statisticians from the planet Tvaaarn.
QI Psi is now operating on the Ninth Plane, Level Four.
See ya there. 




Rory Gilmore

40070. Sat Dec 17, 2005 12:51 pm 


To the intrapsi teleplane device! 




karensell

130395. Sun Dec 31, 2006 5:55 pm 


raindancer wrote:  garrick92
Quite.
You see, I just can't get away from this idea that it's just not possible to understand life through a mathematical or physical science. The theories and experiments are an activity somewhat in isolation from other branches of knowledge. When you're up to your eyes in equations and experiments, you're not actually looking at life!
To understand the whole of something you have to step back from it. The human mind can do this, which I suppose might be called mysticism, but a mind absorbed in theories and maths can't. How can it? One has to be completely unabsorbed...
It may already have been shown that all maths has a limit, and I think that's pretty obvious anyway. Maths, however precise, can only go so far, rather like logic. What they are doing, as far as I know, is breaking life down one piece at a time. It used to be atoms, then particles, now strings and so on. Before long, it might be something else. But will that reveal the secret of life? What happens when they come down to absolutely nothing? Truth may be absolute nothingness!
I'm really not sure that to understand life, the mind mustn't be free of science. I know all this seems very negative. Science certainly has its place, and I'm not knocking it per se, but if they are to really get to the source of it all something else is required. Obviously, there must be a source of energy somewhere. That can be taken for granted, otherwise we wouldn't be here, but it must be a source that is completely beyond everything. I don't know how they are going to come to that, even mathematically, because everything known has a limit. One has to go beond the limit, and that's the problem. 
I have a question!
Could this be the 'source of energy' that broke 2 of my ashtrays in half, while in unoccupied and seperate rooms, when I was pregnant and smoking? 21 years later and it still puzzles me!!!!
First I thought it was my late grandmother, warning me of smoking while pregnant but years later and still a non believer, I kinda think it was more likely to be my own link to an 'unknown source' of energy!!! Who Knows? Hormones? Stress?
Equations and experiments are all part of 'looking at life' but as long as our brains are too complex to fully understand, the secret of life, surely will remain a mystery. 




Celebaelin

1234458. Mon Apr 17, 2017 11:57 am 


4 sets of 10 Card Trials (all today as I've only now registered).
13 hits in 40 trials (approx. 1 in 3)
Probability 22.1:1
A larger sample size might be required  maybe next time I'll do 100. 




Celebaelin

1234590. Tue Apr 18, 2017 11:14 am 


100 today (standard experimental run)
20/100 = 1 in 5 exactly what the odds are but for some reason the probability as calculated by the site is
0.9:1 




Celebaelin

1234769. Wed Apr 19, 2017 5:31 pm 


84/460
4.2 to 1
Overall then 117/600 (or near as dammit 1 in 5). 



