Results 1 to 4 of 4

Math Help - venn

  1. #1
    Junior Member
    Joined
    Oct 2007
    From
    Egypt
    Posts
    35

    venn

    11.give that : P(A)=P(B)=P(C)=1/4,P(AB)=P(CB)=0 and P(AC)=1/8 ,compute the probability that at least one of the three events A,B or C will occur .
    --------------------------------------------------
    12 . suppose that :P(A)=0.4 , P(B)=α ,P(AUB)= 0.7:
    i.what is the value of α which makes A and B disjoint ?
    ii. what is the value of αwhich makes A and B independent ?
    ------------------------------------------------------------
    13 . show that:
    i. P(ABC)=P(A|BC)P(B|C)P(C)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by compufatwa View Post
    11.give that : P(A)=P(B)=P(C)=1/4,P(AB)=P(CB)=0 and P(AC)=1/8 ,compute the probability that at least one of the three events A,B or C will occur .
    Draw a diagram.

    From the diagram it is clear that

    p(A or B or C)= P(A)+P(C)- P(A and C) + P(B).

    RonL
    Attached Thumbnails Attached Thumbnails venn-gash.jpg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,689
    Thanks
    617
    Hello, compufatwa!

    Here's #12 . . .


    12 . Given: . P(A) =0.4,\;P(B)= \alpha,\;P(A \cup B) = 0.7

    a) What is the value of \alpha which makes A and B disjoint?
    We have: . P(A \cup B) \;=\;P(A) + P(B) - P(A \cap B)

    Hence: . 0.7 \;=\;0.4 + \alpha - P(A \cap B) .[1]


    If A and B are disjoint, then P(A \cap B) = 0

    Then [1] becomes: . 0.7 \;=\;0.4 + \alpha - 0\quad\Rightarrow\quad\boxed{\alpha \,=\,0.3}



    b) What is the value of \alpha which makes A and B independent ?

    If A and B are independent, then: . P(A \cap B) \:=\:P(A)\!\cdot\!P(B)

    Then [1] becomes: . 0.7 \;=\;0.4 + \alpha -P(A)\!\cdot\!P(B)\quad\Rightarrow\quad0.7 \;=\;0.4 + \alpha - (0.4)(\alpha)

    Therefore: . 0.3 \:=\:0.6\alpha\quad\Rightarrow\quad\boxed{\alpha \,=\,0.5}

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Oct 2007
    From
    Egypt
    Posts
    35
    thanks lot Soroban and CaptainBlack for this info
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Venn
    Posted in the Discrete Math Forum
    Replies: 17
    Last Post: May 6th 2011, 03:56 PM
  2. Venn Diagrams
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 23rd 2010, 07:35 AM
  3. Venn Diagram
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 9th 2009, 06:12 AM
  4. Venn
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: October 5th 2008, 03:48 PM
  5. Venn Diagrams
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 23rd 2008, 03:29 PM

Search Tags


/mathhelpforum @mathhelpforum