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freckles

  • 2 years ago

A university in Alabama has 1000 employees. Four hundred of the employees have at least 20 years of experience (event A), 100 are African American (event B), and 300 with a background in Microsoft Office 2003 (event C). Assume A,B,C are independent. What is the probability of finding an employee who meets at least two of the three criteria? Answer is suppose to be .166, but how?

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  1. freckles
    • 2 years ago
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    @zarkon :)

  2. freckles
    • 2 years ago
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    I thought I do P(ABC)+P(AB)+P(AC)+P(BC) =P(A)P(B)P(C)+P(A)P(B)+P(A)P(C)+P(B)P(C) but that doesn't work :(

  3. Cloverpetal
    • 2 years ago
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    That should work... hmmmm

  4. BasketWeave
    • 2 years ago
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    Try drawing either a Tree Diagram or a Venn Diagram. You've counted some events (like ABC) more than once.

  5. Cloverpetal
    • 2 years ago
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    agreed^

  6. freckles
    • 2 years ago
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    So how do I draw a venn diagram for independent events?

  7. freckles
    • 2 years ago
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    That would be three separate venn diagrams right?

  8. BasketWeave
    • 2 years ago
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    Oops, yes, you're right. What about Tree Diagrams?

  9. freckles
    • 2 years ago
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    :( I don't know. I'm not seeing it.

  10. BasketWeave
    • 2 years ago
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    OK. I'll draw the Tree and label it, but you fill in the probabilities (on here or on a sheet of paper). Agreed?

  11. freckles
    • 2 years ago
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    Alright!

  12. BasketWeave
    • 2 years ago
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    |dw:1331329425257:dw|

  13. BasketWeave
    • 2 years ago
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    Sorry about the scribble on the right :)

  14. BasketWeave
    • 2 years ago
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    Now just label the branches (ABC, ABC', AB'C, AB'C' etc etc) and fill in the probabilities. Then choose which branches to add up :)

  15. BasketWeave
    • 2 years ago
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    By branch I mean the ones on the right, by the way.

  16. freckles
    • 2 years ago
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    |dw:1331329609363:dw|

  17. freckles
    • 2 years ago
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    \[P(ABC)+P(ABC')+P(AB'C)+P(A'BC)=.012+.028+.108+.018=.166\] omg you are totally awesome

  18. freckles
    • 2 years ago
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    That is a perfect idea. Thanks.

  19. BasketWeave
    • 2 years ago
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    You're welcome!

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