Probablity of the ceiling falling?

Jigar Gosar · 09-20-2007, 04:10 PM

My friend asked me a question. "What is the probability of this 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.

Akavall · 09-20-2007, 05:38 PM

Your friend doesn't give a time frame. Will the ceiling fall in an hour? year? 100 years? The probabilities here are diffrent, the longer the time frame the greater the chance that the ceiling will fall.

A very crude estimate of probablity of a ceiling falling can be obtained by looking at how many ceiling fell in the past. For example, you could look at how many ceilings fell yesterday, and divided that by the number of building. This assumes the building are all equal quility, but this provides a rough estimate for a ceiling falling within 24 hours, and I am sure it is far less than 1/2

.

Jigar Gosar · 09-21-2007, 12:56 AM

Akavall: Thanks for the reply.

I was wondering why do we need a time frame, when we toss the coin, do we need a time frame, to figure whether it will be head or tail? Also if a murder was committed, do we need a time frame to figure out the probability of the murderer being a particular person?

My friends argument is that the probability is 1/2 irrespective of the time. same as in the above two cases.

Secondly, when I gave the similar crude estimation, of considering other ceilings that fell, and then compute the probability. His argument was why don't you do that for the coin then, taking into all coins that were tosses yesterday and then compute the probability?

Every explanation I present, is countered with another such argument. And I am not able to find any concrete flaw in his reasoning.

Please help

Xenu · 09-21-2007, 08:29 AM

Quote:

Originally Posted by Jigar Gosar

My friends argument is that the probability is 1/2 irrespective of the time. same as in the above two cases.

Your friend doesn't seem to understand probabilty.

Waiting a longer time is equivalent to tossing the coin more times. So if you wait a 100 years and the probability for the ceiling to fall each of the years is 1/2 the probabilty for the ceiling to remain intact is the same as the probability to never toss heads in 100 tosses. So clearly the time frame makes a difference.

Quote:

Every explanation I present, is countered with another such argument. And I am not able to find any concrete flaw in his reasoning.

I suggest that you offer your friend a bet. If you toss a dice you can either get a 6, or not get a 6. Now, offer him three times his bet in return if he rolls a six. According to his reasoning the probabilities should be 50/50 so he should clearly take this bet. Let him do this as many times as he want to. Or why not make a bet if the ceiling will fall within the next 10 seconds? Easy money.

Jigar Gosar · 09-21-2007, 01:27 PM

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? exactly which step is incorrect.

Xenu · 09-21-2007, 02:04 PM

He assumes that the probabilities of events always are equal which of course is not the case.

So the statement
p(falling) = no favorable outcome / total outcome.
is false.

Xenu · 09-21-2007, 02:06 PM

Doublepost

Jigar Gosar · 09-21-2007, 02:30 PM

thanks for the reply,

Can u elaborate a bit on it? where did he assume, cause I don't see any assumption in the code? Little explanation will be helpful.

Xenu · 09-21-2007, 02:45 PM

He doesn't state the assumption openly, but the statement:

p(falling) = number of favorable outcome / total number of outcomes.

Is only true if the probability for each event is equal. It's true if you toss a fair die and each possible number is one event. But it is not true if, for example, getting an 1,2,3,4 or 5 is one event and getting a 6 is another event. Then the favourable event (getting a 6) can NOT be calculated by dividing the number of favourable events by the total number of events.

So basically, in order to make his so called proof that the events are equally likely, he assumes that the events are equally likely. Talk about circular reasoning.

Jigar Gosar · 09-22-2007, 09:56 AM

Thanks, a lot for such a clear explanation.

Is has happened couple times, that when I talk abut the applicability of probability in real life, I forget to apply the basic preconditions to use a formula, and end up being puzzled by stupidest of the problem.

When solving text-book problems, such mistakes don't occcur that frequently, where we know the correct path but fail to follow it. But in real world, I have found that, inevitably, time and again, we forget to apply the simplest of knowledge, that can help us solve a problem.

I feel good now, after giving an explanation of why I acted so stupidly and forgot the basics

Thanks a lot Xenu.

09-20-2007, 04:10 PM	#1
Jigar Gosar Junior Member Join Date: Sep 2007 Posts: 5 Thanks: 0 Thanked 0 Times in 0 Posts	Probablity of the ceiling falling? My friend asked me a question. "What is the probability of this 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.

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09-20-2007, 05:38 PM	#2
Akavall Member Join Date: Jul 2007 Posts: 36 Thanks: 0 Thanked 0 Times in 0 Posts	Your friend doesn't give a time frame. Will the ceiling fall in an hour? year? 100 years? The probabilities here are diffrent, the longer the time frame the greater the chance that the ceiling will fall. A very crude estimate of probablity of a ceiling falling can be obtained by looking at how many ceiling fell in the past. For example, you could look at how many ceilings fell yesterday, and divided that by the number of building. This assumes the building are all equal quility, but this provides a rough estimate for a ceiling falling within 24 hours, and I am sure it is far less than 1/2 .

09-21-2007, 12:56 AM	#3
Jigar Gosar Junior Member Join Date: Sep 2007 Posts: 5 Thanks: 0 Thanked 0 Times in 0 Posts	Akavall: Thanks for the reply. I was wondering why do we need a time frame, when we toss the coin, do we need a time frame, to figure whether it will be head or tail? Also if a murder was committed, do we need a time frame to figure out the probability of the murderer being a particular person? My friends argument is that the probability is 1/2 irrespective of the time. same as in the above two cases. Secondly, when I gave the similar crude estimation, of considering other ceilings that fell, and then compute the probability. His argument was why don't you do that for the coin then, taking into all coins that were tosses yesterday and then compute the probability? Every explanation I present, is countered with another such argument. And I am not able to find any concrete flaw in his reasoning. Please help

09-21-2007, 01:27 PM	#5
Jigar Gosar Junior Member Join Date: Sep 2007 Posts: 5 Thanks: 0 Thanked 0 Times in 0 Posts	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? exactly which step is incorrect.

09-21-2007, 02:04 PM	#6
Xenu Senior Member Join Date: May 2007 Posts: 113 Thanks: 0 Thanked 0 Times in 0 Posts	He assumes that the probabilities of events always are equal which of course is not the case. So the statement p(falling) = no favorable outcome / total outcome. is false.

09-21-2007, 02:06 PM	#7
Xenu Senior Member Join Date: May 2007 Posts: 113 Thanks: 0 Thanked 0 Times in 0 Posts	Doublepost

09-21-2007, 02:30 PM	#8
Jigar Gosar Junior Member Join Date: Sep 2007 Posts: 5 Thanks: 0 Thanked 0 Times in 0 Posts	thanks for the reply, Can u elaborate a bit on it? where did he assume, cause I don't see any assumption in the code? Little explanation will be helpful.

09-21-2007, 02:45 PM	#9
Xenu Senior Member Join Date: May 2007 Posts: 113 Thanks: 0 Thanked 0 Times in 0 Posts	He doesn't state the assumption openly, but the statement: p(falling) = number of favorable outcome / total number of outcomes. Is only true if the probability for each event is equal. It's true if you toss a fair die and each possible number is one event. But it is not true if, for example, getting an 1,2,3,4 or 5 is one event and getting a 6 is another event. Then the favourable event (getting a 6) can NOT be calculated by dividing the number of favourable events by the total number of events. So basically, in order to make his so called proof that the events are equally likely, he assumes that the events are equally likely. Talk about circular reasoning.

09-22-2007, 09:56 AM	#10
Jigar Gosar Junior Member Join Date: Sep 2007 Posts: 5 Thanks: 0 Thanked 0 Times in 0 Posts	Thanks, a lot for such a clear explanation. Is has happened couple times, that when I talk abut the applicability of probability in real life, I forget to apply the basic preconditions to use a formula, and end up being puzzled by stupidest of the problem. When solving text-book problems, such mistakes don't occcur that frequently, where we know the correct path but fail to follow it. But in real world, I have found that, inevitably, time and again, we forget to apply the simplest of knowledge, that can help us solve a problem. I feel good now, after giving an explanation of why I acted so stupidly and forgot the basics Thanks a lot Xenu.