 |
|
|
|
|
|
| |
| |
|
|
|
|
| |
| |
|
|
(Not that I plan any more.. but since this is my first stupid
probability question. This is sort of in the vein of Andy's classic
Random Wonderings post series ...Hey, whatever happened to those, Andrew?)
So, here it is. Stupid Probability Question #1:
Suppose you're on a 100 year flood plane. Now ... suppose the last flood
was some 76 years ago in that area. Does the probability of a flood
increase as your approach 100 years, or does the probability of a flood
stay the same?
-OR- is probability irrelevant due to changing conditions?
Obviously insurance companies base their flood insurance rates on the
probability of a flood, and laws are in place to require such insurance
in areas prone to flooding.
This has probably been worked out or answered by someone, I'm sure...
but I'm posting here to provoke some thought and discussion. :) Yeah,
I'm poking the beast with a twig ;)
--
~Mike
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Mike Raiford wrote:
> Hey, whatever happened to those, Andrew?)
Now there's a pretty random wondering!
The answer, of course, is that usually when I think of something, I'm
nowhere near a computer.
For example, just the other day I was on the London Underground, and I
wondered: How the **** do they get the trains onto the track? Something
like the Circle line is completely subterranian, and I'm pretty sure the
factory where they make the carrages isn't. And it's not like you can
just take a train carrage down the escalator with you...
> So, here it is. Stupid Probability Question #1:
>
> Suppose you're on a 100 year flood plane. Now ... suppose the last flood
> was some 76 years ago in that area. Does the probability of a flood
> increase as your approach 100 years, or does the probability of a flood
> stay the same?
>
> -OR- is probability irrelevant due to changing conditions?
In the first analysis, the probability of an event remains constant
regardless of past events. E.g., the probability of rolling a 6 with a
dice is *always* 1/6, regardless of how long it is since the last time
somebody rolled 6 (or any other number).
This analysis works only if events are statistically *independent*, of
course. In the case of a flood, they might not be.
In the second analysis, if a dice is rolled and almost never turns up a
6, this could be taken as evidence that the dice is biased, in which
case the probability is not actually 1/6.
In the case of a dice, we can analytically compute what the probability
"should be". In the case of a flood, presumably you can't. You can only
*estimate* that probability. And it is likely that different estimation
methods will yield different estimates. In short, the "probability"
becomes a rather subjective thing.
On top of all that, of course, probability tells us nothing about when a
particular area will flood. It tells us only how many times it will
flood over a long period of time. Probability only talks about large
numbers, not specific instances.
It is *highly* unlikely that any specific person will win the lottery.
And yet people still win, somehow.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
> For example, just the other day I was on the London Underground, and I
> wondered: How the **** do they get the trains onto the track? Something
> like the Circle line is completely subterranian, and I'm pretty sure the
> factory where they make the carrages isn't. And it's not like you can just
> take a train carrage down the escalator with you...
The Circle line will have connections to other tracks that come up above
ground. There are lots of connections that are not marked on the public
underground map. They are needed for things like train repairs and
replacements, and if some lines have fewer trains during busy periods, they
need somewhere to park the other trains!
> This analysis works only if events are statistically *independent*, of
> course. In the case of a flood, they might not be.
Yep, floods are influenced by things like sun-spots, which follow patterns.
> In the second analysis, if a dice is rolled and almost never turns up a 6,
> this could be taken as evidence that the dice is biased, in which case the
> probability is not actually 1/6.
Also the probability of a flood likely changes dramatically over time,
before you get a chance to calculate a good estimate of the probability.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
scott wrote:
>> For example, just the other day I was on the London Underground, and I
>> wondered: How the **** do they get the trains onto the track?
>> Something like the Circle line is completely subterranian, and I'm
>> pretty sure the factory where they make the carrages isn't. And it's
>> not like you can just take a train carrage down the escalator with you...
>
> The Circle line will have connections to other tracks that come up above
> ground. There are lots of connections that are not marked on the public
> underground map. They are needed for things like train repairs and
> replacements, and if some lines have fewer trains during busy periods,
> they need somewhere to park the other trains!
Yeah, I guess so...
>> This analysis works only if events are statistically *independent*, of
>> course. In the case of a flood, they might not be.
>
> Yep, floods are influenced by things like sun-spots, which follow patterns.
I was thinking more along the lines that a flood might well change the
characteristics of the flooded land / water courses through it, and
these changes may well affect the probability of another flood happening
(although I couldn't say in which direction).
>> In the second analysis, if a dice is rolled and almost never turns up
>> a 6, this could be taken as evidence that the dice is biased, in which
>> case the probability is not actually 1/6.
>
> Also the probability of a flood likely changes dramatically over time,
> before you get a chance to calculate a good estimate of the probability.
Probability is of course relative too.
The probability that the next letter in a sentence is a U is about 2.7%.
However, the probability that the next letter is a U *given that* the
previous letter was Q is more like 90%.
You might argue that that's because these events aren't independent. But
consider that the chance of rolling two 6's is 1/6^2, but the chance of
rolling two 6's *given that* you've already rolled one is 1/6 (i.e., 6
times more probable).
Probability: It depends on what you calculate.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
On 29/06/2010 10:31 PM, Invisible wrote:
>
> For example, just the other day I was on the London Underground, and I
> wondered: How the **** do they get the trains onto the track? Something
> like the Circle line is completely subterranian, and I'm pretty sure the
> factory where they make the carrages isn't. And it's not like you can
> just take a train carrage down the escalator with you...
>
(Referring to the London Underground)
Most lines interconnect and join to the surface network so carriages can
get into and out of the system pretty easily.
The exception is the Waterloo and City line. It has no track connection
to the rest of the system. Carriages (including those with motors) are
lifted in and out through a hatch by a large crane. They are carried on
trucks through the City.
The 'Monster Moves' program has an episode where I think it was 8
carriages had been refurbished and needed to be returned to the line. A
350 ton capacity truck crane was used. Roads were closed and had to be
protected by steel plates on which the crane jacked up.
From memory the carriages were only about 30 ton each but the crane
needed a lot of counterweights because of the long reach required due to
the crane position.
There is more info and a picture of a carriage being lifted on Wikipedia
under 'Waterloo & City line'.
I think I found the access point here:
http://maps.google.com.au/maps?q=51.502025,+-0.110985&num=1&t=k&sll=51.503146,-0.113259&sspn=0.006295,0.006295&hl=en&ie=UTF8&ll=51.502248,-0.110518&spn=0.002528,0.004388&z=18&iwloc=A&layer=c&cbll=51.501955,-0.110964&panoid=GtvSCx6-7JnSbK-1SeGxCQ&cbp=12,349.49,,0,5.08
(Spur Rd near Waterloo Station)
The fixed crane visible there would only be for relatively small
equipment not the carriages.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Mike Raiford wrote:
> (Not that I plan any more.. but since this is my first stupid
> probability question. This is sort of in the vein of Andy's classic
> Random Wonderings post series ...Hey, whatever happened to those, Andrew?)
>
> So, here it is. Stupid Probability Question #1:
>
> Suppose you're on a 100 year flood plane. Now ... suppose the last flood
> was some 76 years ago in that area. Does the probability of a flood
> increase as your approach 100 years, or does the probability of a flood
> stay the same?
>
> -OR- is probability irrelevant due to changing conditions?
The probability is based on historical records, and itself could be off.
If the chances of a flood in any given year are not affected by past
history of floods--and this is presumed to be the case for things like
this--then the chances do not increase with the dry spell.
It is the same principle as, for example, a family with eight children,
all of whom are girls. The parents might think that they are due for a
boy, but the probability of the next child being a girl is the same as
it has been all along.
Regards,
John
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
John VanSickle wrote:
> It is the same principle as, for example, a family with eight children,
> all of whom are girls. The parents might think that they are due for a
> boy, but the probability of the next child being a girl is the same as
> it has been all along.
http://en.wikipedia.org/wiki/Conditional_probability
For something like the roll of a dice where you have all the necessary
information to compute a probability exactly, that works. For something
with unknown variables, seeing an improbable chain of events probably
indicates that you have mis-estimated the variables. (E.g., if you have
eight girls, it could be a total fluke, or there might be an actual
_reason_.)
Probability is a fickle thing. ;-)
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
And lo On Tue, 29 Jun 2010 13:13:47 +0100, Mike Raiford
<"m[raiford]!at"@gmail.com> did spake thusly:
> (Not that I plan any more.. but since this is my first stupid
> probability question. This is sort of in the vein of Andy's classic
> Random Wonderings post series ...Hey, whatever happened to those,
> Andrew?)
>
> So, here it is. Stupid Probability Question #1:
>
> Suppose you're on a 100 year flood plane. Now ... suppose the last flood
> was some 76 years ago in that area. Does the probability of a flood
> increase as your approach 100 years, or does the probability of a flood
> stay the same?
No
> -OR- is probability irrelevant due to changing conditions?
Kind of :-)
As well as the other answers given think of which hundred year span you're
thinking of. If I date it from the last flood then in one hundred years I
have one other flood then in the next hundred years another I have 1 flood
per century. If I start at the same point and have two floods in the first
hundred years and no floods in the second hundred I still have 1 flood per
century.
What in this instance the term means is that you can expect to have just 1
flood per century, if you get more, bad luck and some reassessing of your
insurance might be done. if not good luck; keep paying us the same amount
thank you very much.
It's just as a species we like patterns, we like cycles and we don't like
randomness, so as roughly mentioned if I flip a coin 8 times and it comes
down heads each time the probability of it coming down tails doesn't
increase, but it might mean it decreases as the coin is biased hence the
"kind of" on changing conditions. If it's not biased then over time the
ratio comes out to 1:1, but if I just pick a section of my results it
might not seem that way.
--
Phil Cook
--
I once tried to be apathetic, but I just couldn't be bothered
http://flipc.blogspot.com
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
|
|
