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Author Topic:   Probability - what is it, and how is it used?
nwr
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Posts: 6408
From: Geneva, Illinois
Joined: 08-08-2005
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Message 1 of 2 (302447)
04-08-2006 3:36 PM


This topic is intended to allow the discussion of probability, as suggested in Message 62. The main purpose of this thread is to provide a topic for discussing probability issues that arise in other threads.
Possible subtopics include
  • conditional probability;
  • probabilities where there are many trials;
  • stochastic independence.
    The topic arises in ID and creationist arguments, because such arguments often try to estimate a probability and then claim that since the event is improbably there must have been a creator/designer. It is a common mistake in such arguments to use absolute probabilities where conditional probabilities should be used, and to ignore the factor that there might me many trials.
    For this OP, I will give a brief overview. Other details and subtopics can be brought out in later replies.
    My own view is to take probability as a mathematical theory that turns out to be very useful in modelling real world phenomena, particularly in cases where there is uncertainty.
    In mathematics, we think in terms of a probability space. You can think of that geometrically. For example, if we are throwing darts at a dart board, then we could think of the dart board as the probability space. If we throw a dart, it might hit at some point on the dart board. We can talk of the throwing of the dart as a random trial, and where it hits the dart board as a point in the probability space or as an outcome of the random trial. An event is a set of points in the probability space. The idea is that each possible outcome might be extremely unlikely (have probability zero), but a small region (the "bull's eye" on the dartboard) has a positive probability.
    The probability of an event is a number between 0 and 1, indicating how likely that event will occur. Where the set is the whole of the probability space, the probability is 1. If A and B are two non-overlapping events, then the probability of the combined event (the set A union B) is the sum of the probabilities of A and B).
    The probability of event A is often written as PR(A).
    If A and B overlap, we can talk of the conditional probability of A, given B. This is often written as PR(A|B). It is calculated as
    PR(A intersection B) / Pr(B)
    Intuitively, it is what we should take as the probability that we are right in guessing that A happened, given that we already know that B happened.
    Events A and B are said to be stochastically independent if
    Pr(A|B) = Pr A
    That is, the condition that B occurred has no impact on the probability A occurred.
    (suggest Creation/Evolution Miscellany)

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    AdminModulous
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    Message 2 of 2 (302455)
    04-08-2006 3:54 PM


    Thread moved here from the Proposed New Topics forum.

      
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