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Homework Help: Probability/Statistics Question

  1. Mar 22, 2010 #1
    My brother in law asked me to look at this homework problem for him for a statistics class. He assumes that since I'm taking calculus that I must be able to learn statistics and probability. So I've tried to learn what I can this morning but don't see it going too far.



    1. The problem statement, all variables and given/known data


    Suppose that P(A) = .61, P(B) = .42, and P(A [tex]\cap[/tex] B) = .14

    Calculate the following:

    a) P(A [tex]\cup[/tex] B)

    b.) P(A l B)

    c.) P(B l A)

    d.) P([tex]\bar{A}[/tex] [tex]\cup[/tex] B)

    e.) P(A l [tex]\overline{B}[/tex])

    f.) P([tex]\bar{A}[/tex] l B)


    g) Are A and B independent events? Why or Why not?

    h) Are A and B mutually exclusive events? Why or why not?



    2. Relevant equations



    3. The attempt at a solution

    a) P (A U B) = P(A) + P(B) = .61 + .42 = 1.03. (I feel this is incorrect).

    b) I don't know how to calculate or attempt (AlB)

    d) I don't know what the line over the A means.

    g) The are independent if P(A U B) = P(A)P(B), but .14 not equal to .61 * .42, so not independent.

    h) ?



    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 22, 2010 #2

    tiny-tim

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    Homework Helper

    Hi srfriggen! :smile:

    Use Venn diagrams to find what to add, and what to subtract.

    I guess the bar means "not".

    A and B are independent if P(A and B) = P(A)P(B). :wink:
     
  4. Mar 22, 2010 #3
    so they are not dependent since P(A and B) does not equal P(A)P(B)?

    How do I know if they are mutually exclusive?

    Is the answer to a) .89? P(A)+P(B) - P(A and B)?

    And how do I calculate P(A l B)?



    This seems like an easy problem, IF, I was taking probability or statistics haha. but I just don't have the time to learn it today. I have a calc II test wednesday that is taking up all my time.
     
  5. Mar 22, 2010 #4

    tiny-tim

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    yes
    yes
    Your brother-in-law should know the definitions of P(A l B), and of "mutually exclusive". :wink:
     
  6. Mar 22, 2010 #5
    Ok, I think I figured out a few more. Can you let me know if I am correct?...

    P(A l B) = P(A or B)/P(B) = .14/.42 = .333

    P(B l A) = P(A or B)/P(A) = .14/.61=.229

    - Are A and B independent events? Why or why not?
    No, b/c P(A or B) does not equal P(A)P(B)

    -Are A and B mutually exclusive events? Why or why not?
    No, b/c P(A or B) does not equal Zero.


    I'll let him figure out the other 3 but I wanna make sure I'm sending him the correct answers or I'll never hear the end of it! lol
     
  7. Mar 22, 2010 #6

    tiny-tim

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    Yes, that's all correct, except that every time you've written "or", it should be "and". :wink:
     
  8. Mar 22, 2010 #7
    haha, I keep getting those symbols confused!

    Thanks for your help!
     
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