Results 1 to 2 of 2

Math Help - Interpretation of Probability

  1. #1
    Senior Member Sampras's Avatar
    Joined
    May 2009
    Posts
    301

    Interpretation of Probability

    What interpretation of probability is used when one says that the  P(E) = 0 does not imply that  E will not happen, where  E \in \Gamma (  \Gamma is some sample space and  E is an event in it).

    If we used the relative frequency definition, then this statement would be false.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2008
    From
    Paris, France
    Posts
    1,174
    Quote Originally Posted by Sampras View Post
    What interpretation of probability is used when one says that the  P(E) = 0 does not imply that  E will not happen, where  E \in \Gamma (  \Gamma is some sample space and  E is an event in it).

    If we used the relative frequency definition, then this statement would be false.
    Note that this question is only raised for uncountable probability spaces: otherwise, P(A)=0 iff P(\{a\})=0 for all a\in A, hence A=\emptyset if we exclude (as is natural here) the case when some point has zero probability.

    In particular, the question refers to problems dealing with the infinity, hence the notion of "happening", which evokes the reality of an event, is unclear. The answer may depend on what is considered "possible": is it possible to play heads and tails and get heads indefinitely? This is "infinitely unlikely" but conceivable.

    These unempty events with zero probability are an abstraction, but often make a more concrete sense as a limit: the above example has zero probability because the probability of getting n heads in a row converges to 0 as n grows to infinity. This way, only finite spaces are involved. Of course, this is just a way to hide the infinity under the carpet.

    Anyway, I may be wrong but I think that the interpretations of probability (like the one you are evoking) mostly refer to finite probability spaces.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Interpretation of an Integral
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 4th 2011, 09:21 AM
  2. Interpretation
    Posted in the Statistics Forum
    Replies: 4
    Last Post: April 26th 2011, 05:57 PM
  3. Interpretation of Gradient
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 7th 2011, 11:02 AM
  4. Interpretation and satisfaction
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: January 1st 2011, 03:02 AM
  5. Intergral interpretation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 30th 2009, 05:16 PM

Search Tags


/mathhelpforum @mathhelpforum