Probability over probability

Discussion in 'Scientific Statistics Math' started by Amoz Puu, Jul 21, 2003.

  1. Amoz Puu

    Amoz Puu Guest

    Say there are 1 million pebbles. Some black and some are white.

    You take 100. 50 are blacks, 50 are white. What is the probability
    that another one is black?

    You take 100, all 100 are blacks, what is the probability that another
    one is black?

    You take 1, that one is black. What is the probability that another
    one is also black?

    We are taught to estimate the probability of something based on its
    frequency.

    For example, if we do 100 experiment and 100 are black, than the
    probability that everything is black is 100/100=1. However, this
    estimate also has uncertainty. It is possible that we happen to take
    100 black pebbles. It is possible that the rest are white and only 100
    are black, and the 100 that we pick happen to be the black ones. This
    issue raise in live a lot where people are basing their map on the
    world on their experiences and there is only so much data.

    So, how do we deal with this probability within probability? Do we say
    that if we do 100 experiment and 100 are black, than the probability
    of the next one is black would be 99%? I mean it should be less than
    100% but it should be close to 1 because so far all are black right?

    What would be the formula? Can I extend it to few cases? What about if
    someone take 1 pebbles and found a black one?
     
    Amoz Puu, Jul 21, 2003
    #1
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  2. Amoz Puu

    Duncan Smith Guest

    Have a Google for Bayes Rule.

    Duncan
     
    Duncan Smith, Jul 21, 2003
    #2
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  3. Amoz Puu

    Ron Larham Guest

    You need to lookup Bayes theorem/Baysian ststistics

    RonL
     
    Ron Larham, Jul 21, 2003
    #3
  4. For probability theory to apply to real world problems two
    conditions must exist.

    First, all the elements in the population in question must
    be homogeneous, for example, only marbles, not part marbles
    and part beads, when evaluating the distribution of the
    colors of marbles.

    The second requirement is that the population must be truly
    randomized, i.e., each element in the population must have
    equal likelihood of selection [and how often does this
    condition truly occur in the real world?].

    Only then will all those probability equations truly apply!

    Good luck!

    WDA

    end
     
    W. D. Allen Sr., Jul 21, 2003
    #4
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