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Math Help - prove or disprove complement of probability

  1. #1
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    Exclamation prove or disprove complement of probability

    I need to prove or disprove (E « F') = 1- Pr(E') - Pr(F) . I'm not deeply familiar with probability theory besides the axioms and theorems. I'd be happy with a good start or hint and can hopefully solve it from there.

    Thank you!


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  2. #2
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    Here is a counterexample.
    Let P(E)=0.4,~P(F)=0.6,~P(E\cap F)=0.2 then it follows that P(E\cap F')=0.2.
    But  P(E\cap F') \not=1-P(E')-P(F)=1-0.6-0.6
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  3. #3
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    P(E\cap F')=0.2
    ...how do you calculate that value? I'd assume Pr(F') - Pr(E) ?
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  4. #4
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    Quote Originally Posted by nikie1o2 View Post
    P(E\cap F')=0.2
    ...how do you calculate that value? I'd assume Pr(F') - Pr(E) ?
    P(E) = P(E \cap F) + P(E \cap F')\; \Rightarrow \;P(E \cap F') = P(E) - P(E \cap F)
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  5. #5
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    Ok heres another question for you! How do you know these are equal? What is the proof behind it... P(E) = P(E \cap F) + P(E \cap F')\; \Rightarrow \;P(E \cap F') = P(E) - P(E \cap F) . i know im picky but i need to document every step. thank you again
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  6. #6
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    Quote Originally Posted by nikie1o2 View Post
    Ok heres another question for you! How do you know these are equal? What is the proof behind it... P(E) = P(E \cap F) + P(E \cap F')\; \Rightarrow \;P(E \cap F') = P(E) - P(E \cap F) . i know im picky but i need to document every step. thank you again
    How do I know that this is true?
    Well for one, I know the basic axioms of probability.
    That does not seem to be the case as far as you are concerned.
    Am I mistaken there?
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  7. #7
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    I'm just confused because if you draw a venn diagram.
    (E \cap F) + (E \cap F') doesnt equal E , it's equals the universe- F ?
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  8. #8
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    You have a long way to go.
    Good luck.
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