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Math Help - Probability prop.

  1. #1
    Member kezman's Avatar
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    Probability prop.

    1) A1 A2 be two events, show that P (A1 ∩ A2) ≤ P (A1) . P (A2)
    2) show that P (A1 ∩ A2 ∩ ... ... An) ≤ P (A1) . P (A2) . ... ... ... ... P (An)
    4)
    show that P (A + B) + P (/ A + / B) = 1

    I have problems with these exercises. I dont know if I copied them wrong.
    thanks
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  2. #2
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    Re: Probability prop.

    1) isn't true. Are you sure you have copied the exercise correctly?
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  3. #3
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    Re: Probability prop.

    Quote Originally Posted by kezman View Post
    1) A1 A2 be two events, show that P (A1 ∩ A2) ≤ P (A1) . P (A2)
    This false. Consider the set \mathbb{D}=\{0,1,2,3,4,5,6,7,8,9\}
    Pick one of those digits at random.
    Let A_1 be the event "that digit is prime".
    Let A_2 be the event "that digit is odd".

    What are \mathcal{P}(A_1),~\mathcal{P}(A_2),~\&~\mathcal{P}  (A_1\cap A_2)~?
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  4. #4
    Member kezman's Avatar
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    Re: Probability prop.

    Quote Originally Posted by Plato View Post
    This false. Consider the set \mathbb{D}=\{0,1,2,3,4,5,6,7,8,9\}
    Pick one of those digits at random.
    Let A_1 be the event "that digit is prime".
    Let A_2 be the event "that digit is odd".

    What are \mathcal{P}(A_1),~\mathcal{P}(A_2),~\&~\mathcal{P}  (A_1\cap A_2)~?
    1/2*4/10<3/10
    4/20<3/10
    2/10<3/10

    thanks plato
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