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Math Help - Basic Probability concept

  1. #1
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    Basic Probability concept

    Sir,I want the proof of the probability theorem P(A and B) = P(A).P(B) where events A and B are indipendent,the number of event points of A = l ,that of B = m with n number of common event points.
    Last edited by spdas; September 2nd 2009 at 04:23 AM. Reason: To clarify some mistakes.
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  2. #2
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    probability axioms

    Hi there

    Your question is an interesting one and I am a little puzzled as to why I myself have not considered this basic question! I had to look into this so I am not 100% sure of the answer but here is my best attempt;

    As with all theories we often start with axioms that are simply stated or defined and accepted. All other theories derive from these.

    If the sample space \Omega has N<\infty elements, i.e A,B C .. etc where A can contain one or more elementary outcomes then the classical axioms of probability according to Kolmogorov are;

    Let A and B be any events then

    P(A)\geq0,
    P(\Omega)=1
    P(A\cup B)=P(A)+P(B) when A\cap B=\oslash.

    The definition of conditional probability
    P(A|B)=\frac{P(A\cap B)}{P(B)} satisfies the above axioms.

    We can state intuitively that if knowing B does not affect A, i.e P(A|B)=P(A), then from the conditional probability definition we can state that
    P(A)=\frac{P(A\cap B)}{P(B)}
    which leads to the multiplication of independent events.

    Thus as far as I can see the independent events that multiply comes directly from the definition of conditional probability. If we were to make another definition then this might change.
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