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    • Thread Starter

    I'm stuck on 3 questions, I'll post the questions and my answers. If anyone could look over them and see any errors or how I could proceed it would be much appreciated. Thanks. Jon.

    Prove that if A and B are events then


    1. P(A intersection B) >= P(A) + P(B) - 1

    My answer

    P(A union B) = P(A) + P(B) - P(A intersection B)
    so rearranging
    P(A intersection B) + P(A) + P(B) - P(A union B)
    substituting back into the original equation
    P(A) + P(B) - P(A union B) >= P(A) + P(B) -1
    P(A union B) <=1


    2. P(A triangle B) = P(A) + P(B) - 2P(A union B)

    I have no idea how to prove this, I drew a Venn diagram and can easily see that it is correct, but am unsure how to prove it by a series of statements.

    3rd question

    I don't really understand what I have to do in this question

    Let S = {1,2,3,...,10}
    and for A = {a1,a2,...,ar} C S (where C is underlined meaning A is a subset of S)

    define a probability by

    P(A) = (a1+a2+...+ar) / (55).

    We could equally write this as

    P(A) = 1/55 sigma a (with a is an element of A underneath the sigma)

    Verify that this satisfies the axoims for probability.

    Sorry about the length. Jon.
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Updated: October 16, 2006

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