Can you calculate probability with infinite sets?

In summary, the conversation discusses the calculation of the probability of choosing an odd number from two sets, A and B, defined as the even integers and the set where for every even integer there are two odd integers respectively. The individual inquires about the possibility of calculating this probability without an appropriate probability distribution, to which the expert responds that a probability distribution must be specified in order to provide a probability for something to happen. The expert also mentions that there is no natural probabilistic method for selecting a member from a countably infinite set. However, if one were to choose uniformly from a countably infinite set such as {2,3,3',4,5,5',...10^20}, the probability of selecting an odd number would
  • #1
gamow99
71
2
Suppose set A is defined as the even integers and set B is defined as for every even integer there are two odd integers, like so: {2,3,3,4,5,5,6,7,7 ... }

Can you calculate that the probability of choosing an odd number is 66%?
 
Physics news on Phys.org
  • #2
Not without an appropriate probability distribution.
 
  • #3
Don't know what you mean.
 
  • #4
In order to give a probability for something to happen you need to specify the probability distribution for the possible outcomes.
 
  • #5
gamow99 said:
Don't know what you mean.
Then you should not have used the Intermediate classification for your thread. There is no natural probabilistic method for selecting a member from a countably infinite set.
If you choose uniformly from {2,3,3',4,5,5', ... 10^20) then the probability of selecting an odd is very close to 2/3. The uniform distribution is natural for a finite set, but there is no such for the infinite case.
 
  • Like
Likes Demystifier

1. Can you calculate probability with infinite sets?

Yes, probability can be calculated with infinite sets as long as the set is well-defined and all possible outcomes are equally likely. However, the calculation process may be more complex compared to finite sets.

2. How is probability calculated for infinite sets?

The probability for an event in an infinite set is calculated by dividing the number of outcomes of the event by the total number of outcomes in the set. This is similar to the calculation for finite sets, but may require the use of limits and other mathematical tools.

3. Can the probability of an event in an infinite set be greater than 1?

No, the probability of an event in an infinite set cannot be greater than 1. This would mean that the event is certain to occur, which is not possible for any event in a probabilistic system.

4. Is it possible to have a probability of 0 for an event in an infinite set?

Yes, it is possible to have a probability of 0 for an event in an infinite set. This would mean that the event is impossible to occur. However, it is important to note that a probability of 0 does not necessarily mean that the event will never occur.

5. What are some examples of infinite sets used in probability calculations?

Some examples of infinite sets used in probability calculations include the set of all real numbers, the set of all possible outcomes in a continuous system such as time or distance, and the set of all possible permutations of a set of objects.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
22
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
22
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
5
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
13
Views
961
  • Set Theory, Logic, Probability, Statistics
Replies
13
Views
2K
Replies
15
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
335
  • General Math
Replies
17
Views
563
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
910
  • Set Theory, Logic, Probability, Statistics
Replies
11
Views
499
Back
Top