Question about probability

[Dissipate]

I was thinking about probability and I thought of this. If you have a sample space of infinite events, does that mean that any event in that sample space has a 0 chance of ocurring?

 

[AgaBoogaBoo]

1 in infinite chance

If you think .9 repeating = 1, then yes, would be 0 I imagine assuming you think .0000000000...00001 equals 0

 

[Dissipate]

Originally posted by: AgaBoogaBoo
1 in infinite chance

If you think .9 repeating = 1, then yes, would be 0 I imagine assuming you think .0000000000...00001 equals 0

So suppose you had a bag of infinite things and you reached in and pulled something out. According to that logic that thing just cannot be pulled out of the bag because it has 0 chance of being pulled. But it must be pulled out if you reach in and grab it.

In other words, even if some event must occur within the sample space it still has 0 chance of doing so?

 

[UncleWai]

Use the normal distribution for example, P(x=X) is 0. It's like those calculus reasoning, you need a really small interval to have a probability.

 

[Dissipate]

Originally posted by: UncleWai
Use the normal distribution for example, P(x=X) is 0. It's like those calculus reasoning, you need a really small interval to have a probability.

I guess technically you would have to say that it is the limit as it goes to infinity.

But what I am saying is that suppose you really did have a sample space containing an infinite number of events? Perhaps this is more of a philosophical question.

 

[hypn0tik]

Well, if you have a sample space with an infinite number of events, the probability of a particular event occurring is zero. I guess you can view the probability of a particular event happening to be infinitesmally small, but the summation of all these infinitesmal probabilities will give you 1, the probability of the sample space.

For all intents and purposes, the probability of any particular event is 0. However, there are some methods to calculate probabilities with a sample space of infinite dimension.

For example, consider the interval [0,1]. Now, pick a number from the interval. The probability of you picking a particular x is zero. However, the probability of picking x contained in [a,b] for 0 < a < b < 1 is (b - a)/1, where 1 is the length of the interval.

Essentially what this is saying is that the probability that you pick x = 0.05 is 0, but the probability that you pick x in [0, 0.1] = 1/10

Does that help at all?

 

[Goosemaster]

1/infinity.... which approaches zero...

so the probability approaches zero, and if you actionally define the set as the set of all reals, then yes, the probability is zero

 

[hypn0tik]

Originally posted by: Goosemaster
1/infinity.... which approaches zero...

so the probability approaches zero, and if you actionally define the set as the set of all reals, then yes, the probability is zero

What set are you talking about?

 

[Suspicious-Teach8788]

It is 0. It's just like probability when we talk about.... What is the probability that Kobe played exactly 38:51 in last night's game even if thats what Yahoo sports says.. it's 0, because you can't ever get exactly that much

 

[OdiN]

All probabilities are 50%. Either an event will occur, or it will not.

 

[hypn0tik]

Originally posted by: OdiN
All probabilities are 50%. Either an event will occur, or it will not.

So the probability of getting a 1 after rolling a fair die is 50%? Not quite.

You are probably (no pun intended), thinking of Bernoulli Trials, where a 'success' is defined, and the outcome is either a success or failure. (Note that the probability of success is not necessarily 50%).

 

[OdiN]

Originally posted by: hypn0tik

Originally posted by: OdiN
All probabilities are 50%. Either an event will occur, or it will not.

So the probability of getting a 1 after rolling a fair die is 50%? Not quite.

You are probably (no pun intended), thinking of Bernoulli Trials, where a 'success' is defined, and the outcome is either a success or failure. (Note that the probability of success is not necessarily 50%).

No. 50%. You will either roll a 1 or you will not.

 

[hypn0tik]

Originally posted by: OdiN

Originally posted by: hypn0tik

Originally posted by: OdiN
All probabilities are 50%. Either an event will occur, or it will not.

So the probability of getting a 1 after rolling a fair die is 50%? Not quite.

You are probably (no pun intended), thinking of Bernoulli Trials, where a 'success' is defined, and the outcome is either a success or failure. (Note that the probability of success is not necessarily 50%).

No. 50%. You will either roll a 1 or you will not.

Sorry, try again. There is a 1/6 chance that you will roll a one and a 5/6 chance you will not.

 

[OdiN]

Originally posted by: hypn0tik

Originally posted by: OdiN

Originally posted by: hypn0tik

Originally posted by: OdiN
All probabilities are 50%. Either an event will occur, or it will not.

So the probability of getting a 1 after rolling a fair die is 50%? Not quite.

You are probably (no pun intended), thinking of Bernoulli Trials, where a 'success' is defined, and the outcome is either a success or failure. (Note that the probability of success is not necessarily 50%).

No. 50%. You will either roll a 1 or you will not.

Sorry, try again. There is a 1/6 chance that you will roll a one and a 5/6 chance you will not.

Nah. The event occurs or it does not. It's quite simple.

 

[hypn0tik]

Originally posted by: OdiN

Originally posted by: hypn0tik

Originally posted by: OdiN

Originally posted by: hypn0tik

Originally posted by: OdiN
All probabilities are 50%. Either an event will occur, or it will not.

So the probability of getting a 1 after rolling a fair die is 50%? Not quite.

You are probably (no pun intended), thinking of Bernoulli Trials, where a 'success' is defined, and the outcome is either a success or failure. (Note that the probability of success is not necessarily 50%).

No. 50%. You will either roll a 1 or you will not.

Sorry, try again. There is a 1/6 chance that you will roll a one and a 5/6 chance you will not.

Nah. The event occurs or it does not. It's quite simple.

Hahahaha. If only life were that simple.

 

[OdiN]

Originally posted by: hypn0tik

Originally posted by: OdiN

Originally posted by: hypn0tik

Originally posted by: OdiN

Originally posted by: hypn0tik

Originally posted by: OdiN
All probabilities are 50%. Either an event will occur, or it will not.

So the probability of getting a 1 after rolling a fair die is 50%? Not quite.

You are probably (no pun intended), thinking of Bernoulli Trials, where a 'success' is defined, and the outcome is either a success or failure. (Note that the probability of success is not necessarily 50%).

No. 50%. You will either roll a 1 or you will not.

Sorry, try again. There is a 1/6 chance that you will roll a one and a 5/6 chance you will not.

Nah. The event occurs or it does not. It's quite simple.

Hahahaha. If only life were that simple.

There's a 50% chance that it is.

 

[hypn0tik]

Originally posted by: OdiN

Originally posted by: hypn0tik

Originally posted by: OdiN

Originally posted by: hypn0tik

Originally posted by: OdiN

Originally posted by: hypn0tik

Originally posted by: OdiN
All probabilities are 50%. Either an event will occur, or it will not.

So the probability of getting a 1 after rolling a fair die is 50%? Not quite.

You are probably (no pun intended), thinking of Bernoulli Trials, where a 'success' is defined, and the outcome is either a success or failure. (Note that the probability of success is not necessarily 50%).

No. 50%. You will either roll a 1 or you will not.

Sorry, try again. There is a 1/6 chance that you will roll a one and a 5/6 chance you will not.

Nah. The event occurs or it does not. It's quite simple.

Hahahaha. If only life were that simple.

There's a 50% chance that it is.

And there is a 100% chance I'm going to bed now.

Good night.

 

[OdiN]

Originally posted by: hypn0tik

Originally posted by: OdiN

Originally posted by: hypn0tik

Originally posted by: OdiN

Originally posted by: hypn0tik

Originally posted by: OdiN

Originally posted by: hypn0tik

Originally posted by: OdiN
All probabilities are 50%. Either an event will occur, or it will not.

So the probability of getting a 1 after rolling a fair die is 50%? Not quite.

You are probably (no pun intended), thinking of Bernoulli Trials, where a 'success' is defined, and the outcome is either a success or failure. (Note that the probability of success is not necessarily 50%).

No. 50%. You will either roll a 1 or you will not.

Sorry, try again. There is a 1/6 chance that you will roll a one and a 5/6 chance you will not.

Nah. The event occurs or it does not. It's quite simple.

Hahahaha. If only life were that simple.

There's a 50% chance that it is.

And there is a 100% chance I'm going to bed now.

Good night.

Actually only 50%.

 

[DrPizza]

Originally posted by: Dissipate
I was thinking about probability and I thought of this. If you have a sample space of infinite events, does that mean that any event in that sample space has a 0 chance of ocurring?

How about this as an example:
Select a real number at random between 0 and 1.

The probability of any particular event *is* zero.
However, it is impossible to select a real number x at random such that 0 <= x < 1
If you want to select a number with a precision of the nearest tenth, then there are ten such numbers: .0, .1, .2, ... , .9
The probability of any number is 1/10.
If you want precision to the nearest hundredth, the probability is 1/100.

However, if we wish to consider the answer to be .1000000000...0000 with 99 zeros, the probability is 1/10^100.

Nonetheless, as I already said, it is impossible to actually choose *at random* a number between 0 and 1, with infinite precision. As soon as you specify the number of decimal places before the rest of the digits are 0, you have made it a finite set of numbers. How could you ever randomly select a number (at random) and have an infinite number of decimal places? Perhaps, have a computer start with a decimal and randomly insert digits? It would never finish. Thus, as hypnOtic said, you can have a probability of the event being on a certain interval, i.e. a probability of the number being between .40000235 and .40000236.

Also, I hope Odin is just joking around... An event will either occur, or it won't occur. The sum of the probability of it occurring = 1. But, there are a lot more pairs of positive numbers that sum to one besides just .5 and .5.


edit: I may be wrong.... can someone give a counter-example where it is possible for an event to occur with a probability of 0?

 

[DrPizza]

Originally posted by: AgaBoogaBoo
1 in infinite chance

If you think .9 repeating = 1, then yes, would be 0 I imagine assuming you think .0000000000...00001 equals 0

.9 repeating DOES = 1, and the flaw in that logic is that there is "an end" someplace where the 1 is. the difference between .9 repeating and 1 is .000... repeating forever. There is no end, and thus a 1 can never be put in there.

Ditto in this example. The probability is 0.0000...

 

[JDrake]

I did that problem in class once, it came out to like a 4% chance

 

[darkxshade]

Originally posted by: OdiN

Originally posted by: hypn0tik

Originally posted by: OdiN
All probabilities are 50%. Either an event will occur, or it will not.

So the probability of getting a 1 after rolling a fair die is 50%? Not quite.

You are probably (no pun intended), thinking of Bernoulli Trials, where a 'success' is defined, and the outcome is either a success or failure. (Note that the probability of success is not necessarily 50%).

No. 50%. You will either roll a 1 or you will not.

what about the probability of rolling a 1 on a dice(2 dies)... 50%? nope it will not happen

 

[Dissipate]

Originally posted by: DrPizza

Originally posted by: Dissipate
I was thinking about probability and I thought of this. If you have a sample space of infinite events, does that mean that any event in that sample space has a 0 chance of ocurring?

How about this as an example:
Select a real number at random between 0 and 1.

The probability of any particular event *is* zero.
However, it is impossible to select a real number x at random such that 0 <= x < 1
If you want to select a number with a precision of the nearest tenth, then there are ten such numbers: .0, .1, .2, ... , .9
The probability of any number is 1/10.
If you want precision to the nearest hundredth, the probability is 1/100.

However, if we wish to consider the answer to be .1000000000...0000 with 99 zeros, the probability is 1/10^100.

Nonetheless, as I already said, it is impossible to actually choose *at random* a number between 0 and 1, with infinite precision. As soon as you specify the number of decimal places before the rest of the digits are 0, you have made it a finite set of numbers. How could you ever randomly select a number (at random) and have an infinite number of decimal places? Perhaps, have a computer start with a decimal and randomly insert digits? It would never finish. Thus, as hypnOtic said, you can have a probability of the event being on a certain interval, i.e. a probability of the number being between .40000235 and .40000236.

Also, I hope Odin is just joking around... An event will either occur, or it won't occur. The sum of the probability of it occurring = 1. But, there are a lot more pairs of positive numbers that sum to one besides just .5 and .5.


edit: I may be wrong.... can someone give a counter-example where it is possible for an event to occur with a probability of 0?

I'm not sure if I buy that argument. I would just say pick a number between 1 and infinity. Now you are going to get a number even though you may not be able to write it down.

 

[hypn0tik]

Originally posted by: Dissipate

Originally posted by: DrPizza

Originally posted by: Dissipate
I was thinking about probability and I thought of this. If you have a sample space of infinite events, does that mean that any event in that sample space has a 0 chance of ocurring?

How about this as an example:
Select a real number at random between 0 and 1.

The probability of any particular event *is* zero.
However, it is impossible to select a real number x at random such that 0 <= x < 1
If you want to select a number with a precision of the nearest tenth, then there are ten such numbers: .0, .1, .2, ... , .9
The probability of any number is 1/10.
If you want precision to the nearest hundredth, the probability is 1/100.

However, if we wish to consider the answer to be .1000000000...0000 with 99 zeros, the probability is 1/10^100.

Nonetheless, as I already said, it is impossible to actually choose *at random* a number between 0 and 1, with infinite precision. As soon as you specify the number of decimal places before the rest of the digits are 0, you have made it a finite set of numbers. How could you ever randomly select a number (at random) and have an infinite number of decimal places? Perhaps, have a computer start with a decimal and randomly insert digits? It would never finish. Thus, as hypnOtic said, you can have a probability of the event being on a certain interval, i.e. a probability of the number being between .40000235 and .40000236.

Also, I hope Odin is just joking around... An event will either occur, or it won't occur. The sum of the probability of it occurring = 1. But, there are a lot more pairs of positive numbers that sum to one besides just .5 and .5.


edit: I may be wrong.... can someone give a counter-example where it is possible for an event to occur with a probability of 0?

I'm not sure if I buy that argument. I would just say pick a number between 1 and infinity. Now you are going to get a number even though you may not be able to write it down.

Careful. The probability that you pick a particular number from the set [1,infinity) is 0.

 

[UncleWai]

Odin needs a new math teacher, that sh!t is wacked.


At the end, you just run back to the same problem of 1/n as n approaches infinity.