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Math Help - [SOLVED] Card statistics

  1. #1
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    [SOLVED] Card statistics

    Number 1

    Which are always true?
    * P(SUT)=P(S)+P(T)
    If S is a subset of T, P(SUT)=P(S)
    P(not S)=100%-P(S)
    * If S is a subset of T, P(ST)=P(S)
    * If S is a subset of T, P(SUT)=P(T)


    Number 2
    T implies not S. Which are always true?

    not S is a subset of T
    not T is a subset of S
    * S and T are mutually exclusive
    *S and T are independent
    *not T is a subset of not S



    Number 3
    P(S) = 90% and P(T) = 55%

    Which are always true?
    *P(ST)>=45%
    P(SUT)>=95%
    *T cannot imply S
    S and T cannot be mutually exclusive
    P(SUT)>=90%



    * = ones I think are true


    >>>>Can somebody explain which ones I got wrong? <<<
    Last edited by Starry; July 26th 2009 at 08:38 PM.
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  2. #2
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    Hello, Starry!

    * = ones I think are true

    Number 1:

    Which are always true?


    (a)\;\;P(A \cup B)\:=\:P(A)+P(B)

    (b)\;\;\text{If }A \subset B,\;\text{ then }P(A \cup B)\:=\:P(A)

    (c)\;\;P(\sim A)\:=\:100\% -P(A) *

    (d)\;\;\text{If }A \subset B,\;\text{ then }P(A\cap B)\:=\:P(A) *

    (e)\;\;\text{If }A \subset B,\:\text{ then } P(A\cap B)\:=\:P(B)

    (f)\;\;\text{For any event }A\!:\;P(A) \,\geq\, 0 *

    (g)\;\;P(A\cap B)\: \leq\:P(A) *

    (h)\;\;\text{If }A\cap B\:=\: \emptyset,\:\text{ then }P(A\cup B) \:=\: P(A) +P(B) *

    (i)\;\;P(A \cap B) \:=\:P(A)\!\cdot\!P(B)

    (j)\;\;P(S)\:=\:100\% *

    (k)\;\;\text{If }A \subset B,\:\text{ then }P(A \cup B)\:=\:P(B) *

    (l)\;\;P(A \cup B) \:\leq \:P(A)+P(B) *

    (m)\;\;P(A \cup B) \:=\:P(A)+P(B)-P(A \cap B) *

    All correct . . . Good work!

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  3. #3
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    How about problems 2 and 3?

    I'm sure my answers for 2 are wrong :P
    Last edited by Starry; July 19th 2009 at 07:47 AM.
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  4. #4
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    Quote Originally Posted by Starry View Post
    How about problems 2 and 3?
    2 looks correct. What part are you not sure about?

    I see a problem with 3a.
    P(A)+P(B)-P(AB)\le 1.
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  5. #5
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    I see...!

    so because 90+55-P(ST) <1,
    P(ST) would have to be greater than 45!


    Thanks!
    Also for problem 3, S and T cannot be mutually exclusive right?


    How about problem 2?
    [thank you sooo much for helping!!! ]
    Last edited by Starry; July 19th 2009 at 08:41 AM.
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