+ Reply to Thread
Results 1 to 2 of 2

Thread: Apparent contradiction with the definition of probability

  1. #1
    Points: 12, Level: 1
    Level completed: 23%, Points required for next Level: 38

    Posts
    1
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Apparent contradiction with the definition of probability




    Hi everyone, here is my doubt: according to the definition of probability the probability that in a coin tossing the result be heads is 0.5 because in the limit of infinite trials (n==>infinity) half of times will be obtained heads. This is equivalent to say that in such a limit the probability of getting equal number of heads and tails is one and zero for any other combination. However, the de Moivre–Laplace theorem states that the binomial distribution tends to a normal one with SD √np(1-p) as n goes to infinity, where p is the succes probability that is 0.5 in this case. That would imply that the SD also tends to infinity! and not to zero as is expected from the aforementioned reasoning.

    Thank you very much for your help

  2. #2
    Devorador de queso
    Points: 95,866, Level: 100
    Level completed: 0%, Points required for next Level: 0
    Awards:
    Posting AwardCommunity AwardDiscussion EnderFrequent Poster
    Dason's Avatar
    Location
    Tampa, FL
    Posts
    12,936
    Thanks
    307
    Thanked 2,630 Times in 2,246 Posts

    Re: Apparent contradiction with the definition of probability


    There is a difference between "the number of heads" and "the proportion of heads".

    Note that the SD of the proportion of heads is \sqrt{p(1-p)/n} which goes to 0 as n goes to infinity.
    I don't have emotions and sometimes that makes me very sad.

+ Reply to Thread

           




Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts






Advertise on Talk Stats