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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- freckles

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- freckles

@zarkon :)

- freckles

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 :(

- anonymous

That should work... hmmmm

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## More answers

- anonymous

Try drawing either a Tree Diagram or a Venn Diagram. You've counted some events (like ABC) more than once.

- anonymous

agreed^

- freckles

So how do I draw a venn diagram for independent events?

- freckles

That would be three separate venn diagrams right?

- anonymous

Oops, yes, you're right. What about Tree Diagrams?

- freckles

:( I don't know. I'm not seeing it.

- anonymous

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

- freckles

Alright!

- anonymous

|dw:1331329425257:dw|

- anonymous

Sorry about the scribble on the right :)

- anonymous

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 :)

- anonymous

By branch I mean the ones on the right, by the way.

- freckles

|dw:1331329609363:dw|

- freckles

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

- freckles

That is a perfect idea. Thanks.

- anonymous

You're welcome!

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