Probablity of the ceiling falling?
zEO
ceiling falling?" I was puzzled. Then he replied that the probability
is 1/2. Here is his explanation:
Event1= the ceiling fell.
Event2= the ceiling did not fall.
since there are only two possible outcomes, once favorable and other
unfavorable, hence probability of ceiling falling is 1/2.
I know this conclusion is wrong, but I wasn't able to show to him
where is the flaw in his logic. Can you help me figure out where did
he go wrong.
Art
The P = 1/2 is only valid for equiprobable outcomes such as a
flip of a fair coin. You can't apply this to outcomes that are not
equally probable. Ask your friend how he determined that it's
equally probable that the ceiling will fall or not fall :)
Art
zEO
outcome1 = the ceiling fell. (favorable)
outcome2 = the ceiling did not fall.
p(falling) = no favorable outcome / total outcome.
p(falling) = 1/2
Can u find any flaw in above computation?
On Sep 21, 3:20 am, Art <n...@zilch.com> wrote:
Art
>The thing is that, he proved it mathematically.
>
>outcome1 = the ceiling fell. (favorable)
>outcome2 = the ceiling did not fall.
>
>p(falling) = no favorable outcome / total outcome.
>p(falling) = 1/2
>
>Can u find any flaw in above computation?
Sure. The 1/2 has not been justified or proven. It may be that
at some point in time it so happens that the old building has
become so weak that there is a 50-50 chance of the ceiling
falling. But how does your friend know that exact
point in time (and all the other conditions) with certainty?
It may be that currently the probability of the ceiling
falling is 1/16 or 1/32 or ... whatever.
It's a misapplication of something meant to be applied to
random phenomena such as a coin toss.
Art
Mike Terry
news:1190350978.7...@q5g2000prf.googlegroups.com...
> The thing is that, he proved it mathematically.
>
> outcome1 = the ceiling fell. (favorable)
> outcome2 = the ceiling did not fall.
>
> p(falling) = no favorable outcome / total outcome.
The previous statement is wrong. (As Art pointed out in earlier reply,
including some reasoning as to why.) If your friend claims it is true, it
is up to your friend to present a proof of this, not your responsibility to
disprove it!
This is the flaw in the computation.
zEO
WHERE is the flaw in the following solution. Because we all know that
probability of ceiling falling is not 1/2. But why cant this same
logic be applied to coin tossing, but not to ceiling falling?
outcome1 = the ceiling fell. (favorable)
outcome2 = the ceiling did not fall.
p(falling) = no favorable outcome / total outcome.
p(falling) = 1/2
compare the above scenario to toss of a coin. Has the 1/2 probability
justified or proven for "tail" or "head" ? yes it has been proven, but
in the exact same way in which my friend is trying to prove that of
the ceiling falling. Do we consider the age of the coin, the fragility
of the coin, the direction of the wind and the flip of the finger,
when we try to find the probability of "head" or "tail" for a coin.
No, we don't. Then why do we need to consider the fact such as age of
the building and all the other factors, when we are talking about the
ceiling. Do the above mentioned factors, affect the outcome of the
coin toss? and even if they do, we never account for them in the
calculation of the probability, then why do we consider other external
factors for ceiling.
I hope I have made myself clear, understand this, I believe that
probability for ceiling falling is not 1/2, but I really want to be
sure of its mathematical validity, by comparing it to the toss of a
coin. Even for a toss of coin, we actually go with a proof, the two
events head and tail, same for "ceiling falling" and "not falling".
For the coins we don't consider what time are we tossing, Monday,
Tuesday or a particular time. or whether is the coin old or new etc.
Than why do we do consider this and many other factors for ceiling?
Art: you mentioned that
" It may be that
at some point in time it so happens that the old building has
become so weak that there is a 50-50 chance of the ceiling
falling. But how does your friend know that exact
point in time (and all the other conditions) with certainty? "
My friend has figured out that there is 50-50 %chance of building
falling by applying the above formula, since we have applied the same
formula to compute the prob of coin, (head or tail). How do we know
that head and tail have 50% chance? by applying the above formula.
In the light of the above explanation, can u tell me why one can apply
this logic to coin but not to ceiling?
Dan
> p(falling) = no favorable outcome / total outcome.
> p(falling) = 1/2
Ask your friend to make a bet on whether or not the ceiling will fall.
If he really believes the chances that it will fall are 50%, he should
be more than willing to take 3:1 odds. Of course, you have to set a
time frame such as "by the end of the month". If he's not willing to
take the bet, than it's clear that he doesn't *really* believe the
probabilities he has assigned.
In fact, statistical theory is notoriously silent on questions of this
sort. Statistical theory tells us how to update our beliefs on the
basis of data. In this case, you don't have any data, so the only
thing you have to go on is your prior belief. But in general
statistics does NOT tell us how to obtain priors.
Laplace ran afoul of this when he attempted to predict the probability
of the sun rising tomorrow by calculating the number of days in a row
the sun had risen (say N) and predicting that the prob of the sun not
rising is 1/N. It works if you accept his particular choice of prior,
but there's no clear reason to do so.
Dan
Art
>The question is not WHY the solution presented below is incorrect, but
>WHERE is the flaw in the following solution. Because we all know that
>probability of ceiling falling is not 1/2. But why cant this same
>logic be applied to coin tossing, but not to ceiling falling?
>
>outcome1 = the ceiling fell. (favorable)
>outcome2 = the ceiling did not fall.
>
>p(falling) = no favorable outcome / total outcome.
>p(falling) = 1/2
>
>compare the above scenario to toss of a coin. Has the 1/2 probability
>justified or proven for "tail" or "head" ?
The 1/2 assumes a hypothetical "fair" coin which should, after
a very large number of tosses, N , result in very nearly N/2 heads and
N/2 tails. In other words, randomness is assumed in both the coin
and the tosses.
>yes it has been proven, but
>in the exact same way in which my friend is trying to prove that of
>the ceiling falling. Do we consider the age of the coin, the fragility
>of the coin, the direction of the wind and the flip of the finger,
>when we try to find the probability of "head" or "tail" for a coin.
>No, we don't.
Yes we do. We apply the math to "real world" alleged random
number generators and test them for randomness using
statistical methods.
>Then why do we need to consider the fact such as age of
>the building and all the other factors, when we are talking about the
>ceiling. Do the above mentioned factors, affect the outcome of the
>coin toss?
Sure. The example of the coin toss is hypothetical and based
on the assumption of randomness.
>and even if they do, we never account for them in the
>calculation of the probability, then why do we consider other external
>factors for ceiling.
We account for "real world" lack of randomness in alleged
random number generators by testing them.
>I hope I have made myself clear, understand this, I believe that
>probability for ceiling falling is not 1/2, but I really want to be
>sure of its mathematical validity, by comparing it to the toss of a
>coin. Even for a toss of coin, we actually go with a proof, the two
>events head and tail, same for "ceiling falling" and "not falling".
>For the coins we don't consider what time are we tossing, Monday,
>Tuesday or a particular time. or whether is the coin old or new etc.
>Than why do we do consider this and many other factors for ceiling?
See above.
>Art: you mentioned that
>" It may be that
>at some point in time it so happens that the old building has
>become so weak that there is a 50-50 chance of the ceiling
>falling. But how does your friend know that exact
>point in time (and all the other conditions) with certainty? "
>
>My friend has figured out that there is 50-50 %chance of building
>falling by applying the above formula, since we have applied the same
>formula to compute the prob of coin, (head or tail). How do we know
>that head and tail have 50% chance? by applying the above formula.
>
>In the light of the above explanation, can u tell me why one can apply
>this logic to coin but not to ceiling?
The coin example is a hypothetical based on the assumption of
randomness. By definition, a ideal coin toss results in heads
half the time and tails half the time. You can't say that about
ceilings :)
Art
Pavel314
> The question is not WHY the solution presented below is incorrect, but
> WHERE is the flaw in the following solution. Because we all know that
> probability of ceiling falling is not 1/2. But why cant this same
> logic be applied to coin tossing, but not to ceiling falling?
>
> outcome1 = the ceiling fell. (favorable)
> outcome2 = the ceiling did not fall.
>
> p(falling) = no favorable outcome / total outcome.
> p(falling) = 1/2
Outcome1, the ceiling falling, does represent 1/2 of the possible types of
outcomes defined in the statement. However, that does not mean that it
represents the probability of that particular outcome occurring.
We could easily define a third category to the problem:
> outcome1 = the ceiling fell. (favorable)
> outcome2 = the ceiling did not fall, it remained as it was
> outcome3 = the ceiling sagged in the middle but did not fall
Now the probability of the ceiling falling, under your friend's logic, would
be only 1/3. If we add outcome 4, the ceiling becomes mildewed, his odds of
falling would be reduced to only 1/4.
The odds of the ceiling falling, a specific outcome, should be constant
regardless of how we define the possible outcomes. To me, this is a reductio
ad absurdum refutation of your friend's odds.
Paul
zEO
flaw in the afore discussed calculations. Some of you have given
theories/reasoning , which make an analytical and logical appeal to
our intellect, begging us not to apply the same computation to coin
and ceiling. But my mind has a counter-argument to most of them.
For eg. PAvel314 introduced one more, outcome3, which i can do the
same for a coin, what if, because of a natural disaster, and makeup of
coin, the coin breaks up into two pieces in air, and when it settles
on ground, half is head and other half is tail. I can add even one
more outcome to the coin toss, what if the coin falls and stays on its
side. then there is no head or tail.
Also we never considered the time frame for the toss of a coin. Then
why for ceiling?
My only point is that such arguments, of time and extra outcomes don't
necessarily prove that the calculation is flawed. Even though they
give food for thought and support the fact that the prob for ceiling
falling is not 1/2.
I am guilty of starting a parallel thread on a another forum. And I
have to say that "Xenu" there has clearly pointed out the flaw in the
computation. Although, he didn't give us any newer information than
that we have already touched upon in our discussion here, he gives a
precise reason why the same calculation that can be applied to coin
cannot be applied to ceiling falling.
The answer is simple, in order to use the afore mentioned
calculations, all the events must be equi-probable. We have to first
prove that events are equi-probable, only then we can apply the
questioned calculation.
Equi-probable, as we all know, need not be 1/2, or 50-50%. Equi-
probable simply states that none of the occurrences should have any
bias that help their outcome. All occurrences must have equal
probability, (may through random distribution, or a completely random
event, which guaranteed no bias, making all outcome equally likely).
In case of coin, our first assumption is that the the coin is
unbiased, i.e. all textbooks explicitly state that "for a given
unbiased coin" or "an unbiased dice". Also, as art mentioned, the
process of tossing of coin is also unbiased, i.e. completely random.
Basically, we humans cant replicate exact same muscle movement, same
height and distance from floor, for every toss, there by removing any
bias of the tossing process and hence the outcome is unbiased (here
there is an implicit assumption that the tosser of the coin is not a
con-artist). Since, in case of toss coin we have removed all the bias,
(atlest 99% of it, don't ask how i calculated this probability), there
by making the ocurrance of head and tail equi-probable, i.e. both
occurrences are equally likely. And once we have proved, or taken
necessary measures to make all the outcomes are equi-probable, we can
use the formula for for computing the probability of the "head"/"tail"
i.e. individual probability.
But in the case of the ceiling, instead of trying to remove any bias
from both the events, there is evidence of bias being present. The
bias are the walls supporting the ceiling, the material of the ceiling
is made, all these biases for the ceiling not to fall. And there is no
bias, except gravity for the ceiling to fall. It is upto the person to
prove that both the events are equi-probable before applying the
formula.
This the exact flaw. :) and here is the alternate thread that I
started for the same question. (http://talkstats.com/showthread.php?
p=8076), Where "Xenu" gave the answer in precise words, which I
expanded upon here.
Art:
Looking back at first of your answers , where you mention equi-
probability, and in the last reply where you talk about randomness of
the tossing of the coin, I figure you are saying the same thing, that
I explained in last few paragraphs. But, I became so clear on the
topic only after reading Xenu's post. I am mentioning this because
equal credit for figuring out the flaw should be given to you, it was
my fault that I couldn't interpret it back then.
Thank you all for your answers, It's been a long time since I had some
intellectual discussion with some intelligent people.
On Sep 22, 5:38 pm, "Pavel314" <Pavel...@NOSPAM.comcast.net> wrote:
> "zEO" <jigar.go...@gmail.com> wrote in message
Mike Terry
> Art:
> Looking back at first of your answers , where you mention equi-
> probability, and in the last reply where you talk about randomness of
> the tossing of the coin, I figure you are saying the same thing, that
> I explained in last few paragraphs. But, I became so clear on the
> topic only after reading Xenu's post. I am mentioning this because
> equal credit for figuring out the flaw should be given to you, it was
> my fault that I couldn't interpret it back then.
>
Personally, I would award credit as follows:
Everyone: credit for figuring out the flaw in your argument
Art: credit for being first to point out this flaw
Zeno: credit for being first to make you understand the flaw.
:)
Mike.
Art
>Thank you all for your answers, It's been a long time since I had some
>intellectual discussion with some intelligent people.
I'm glad you found the help you sought. I find the subject area to be
both fascinating and difficult.
Art
Bill
Bill
Since no time limit was imposed, P(C falls) = 1.
Bill J