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Thread: Probability of union

  1. #1
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    Probability of union

    Hi,
    LET Ai,Bi i=1,2 be sets such that the A's are independent and the B's are independent.
    Also pr(Ai)<=pr(Bi),i=1,2

    prove that Pr(A1UA2)<=Pr(B1UB2)

    Thank's in advance.
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  2. #2
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    Re: Probability of union

    What is the formula for P(XUY) if X and Y are independent?
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  3. #3
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    Re: Probability of union

    I know the formula but how to proceed?
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  4. #4
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    Re: Probability of union

    Then please specifically answer Debsta's question!
    Thanks from Debsta and topsquark
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  5. #5
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    Re: Probability of union

    I will be glad for a clue to the solution.
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  6. #6
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    Re: Probability of union

    Quote Originally Posted by hedi View Post
    Hi,
    LET Ai,Bi i=1,2 be sets such that the A's are independent and the B's are independent.
    Also pr(Ai)<=pr(Bi),i=1,2
    prove that Pr(A1UA2)<=Pr(B1UB2)
    Quote Originally Posted by hedi View Post
    I know the formula but how to proceed?
    Quote Originally Posted by HallsofIvy View Post
    Then please specifically answer Debsta's question!
    You were asked, even politely, to respond to a very simple request. Why the he** did you not? Or is it that you cannot?
    Quote Originally Posted by hedi View Post
    I will be glad for a clue to the solution.
    Do not hold your breath. Answer the question.
    Thanks from topsquark
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  7. #7
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    Re: Probability of union

    I am stuck with proving that x+y-xy<=u+v-uv when x<=uand
    y<=v in (0,1).It is probably simple but somehow i dont come to a solution
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  8. #8
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    Re: Probability of union

    Quote Originally Posted by hedi View Post
    I am stuck with proving that x+y-xy<=u+v-uv when x<=uand
    y<=v in (0,1).It is probably simple but somehow i dont come to a solution
    Thank you for finally replying. Now look at this very nice solution to a very tricky inequally.

    Quote Originally Posted by Plato View Post
    If $\large 0\le a\le x\le 1~\&~0\le b\le y\le 1$ then $\large a+b-a\cdot b\le x+y-x\cdot y$
    Quote Originally Posted by Idea View Post
    $\displaystyle 1-a\geq 1-x \geq 0$

    $\displaystyle 1-b\geq 1-y\geq 0$

    Multiply

    $\displaystyle (1-a)(1-b)\geq (1-x)(1-y)$
    Multiply out both sides. Then multiply through by $-1$.
    Last edited by Plato; Feb 22nd 2019 at 10:00 AM.
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