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Math Help - Intersections and Unions

  1. #1
    Junior Member shannu82's Avatar
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    Intersections and Unions

    For events A and B we have
    P(A) =0.3 P(B) = 0.8 P(A∪B) = 0.9
    a) Find P(A|B) P(A'∩B) P(B'∪A').
    b) Are A and B independent? Why?

    Any help would be appreciated.

    Here is my response that i tried... Am not sure if its correct
    part a)
    P(A|B) = (P(A)P(B))/P(B)
    =0.3
    P(A') 1-P(A) =0.7
    P(B') 1-P(B) = 0.2
    P(A'∩B) = P(A')P(B)=0.56
    P(B'∪A') = P(A')+P(B')=0.9

    part b)
    Case 1
    P(A∩B) = P(A)P(B)=.24
    P(A|B) = P(A∩B)/P(B) =rearrange and find P(A∩B) = 0.24
    Case 2
    P(B|A) = P(B)=0.8
    P(B|A) = P(B∩A)/P(A) = (P(B)P(A))/P(A) =.8

    Since Case 1&2 are both true A&B are independent.
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  2. #2
    MHF Contributor harish21's Avatar
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    You really neeed to check your class notes or text book.

    As a matter of fact, you have been told in one of your previous posts that P(A|B) = \dfrac{P(A \cap B}{P(B)}
    How did you find A \cap B??

    You should have definitely covered topics like unions, intersections, complements, and independent events in your class. Without knowing them, you will never be able to do this correctly!
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  3. #3
    Junior Member shannu82's Avatar
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    Re Arrange that ... In part a) i had to find P(A|B) and i was given P(B) so using that i solved for P(A∩B).. and we do know that P(A∩B) = P(A)P(B) if your asking about part a) and we are given P(A) and P(B)...
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  4. #4
    MHF Contributor harish21's Avatar
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    Your question(a) is asking you to find P(A|B).

    to find that, you first need to figure out P(A∩B)

    My question is: How did you find P(A∩B)?? For that you need to look at your book/notes.

    FYI, P(A|B)=0.3 is not the correct answer.
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  5. #5
    Junior Member shannu82's Avatar
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    Thank you for noticing that! I don't know what i was thinking.... Here is the revised version.... Does this make sense?
    P(A|B) = P(A∩B)/P(B)
    P(A∩B)= P(A∪B)-P(A)-P(B)
    =-0.66

    Which for part 2 makes it dependent.
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  6. #6
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by shannu82 View Post
    Thank you for noticing that! I don't know what i was thinking.... Here is the revised version.... Does this make sense?
    P(A|B) = P(A∩B)/P(B)
    P(A∩B)= P(A∪B)-P(A)-P(B)
    =-0.66

    Which for part 2 makes it dependent


    NO.

    Although these facts are surely in your textbook, I will spend few precious minutes of my life writing these with a hope that you will be able to learn.

    P(A \cup B) = P(A)+P(B)-P(A \cap B)

    and

    Two events are independent if P(A \cap B) = P(A) \times P(B)
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