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October 15th, 2010, 10:46 AM   #1
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Probabilty

A car dealer has 410 cars on lot. 67 are white, 263 have an auto. transmission, 38 have a sun roof, 34 are white and have an auto. transmission, 11 are white and have a sunroof, 20 have an auto. transmission and a sunroof, and 8 are white, have an auto. transmission and don't have a sunroof.

1. How many are not white, don't have an auto. transmission and don't have a sunroof? 410-263-38-67= 42?

2. How many are white, have an auto. transmission and don't have a sunroof? 34-8=26?

These answers seem entirely too simple to me. Any help would be greatly appreciated.
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October 15th, 2010, 11:40 AM   #2
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Re: Probabilty

You subtracted 263 (# with auto. trans.) and 67 (# white) from 410 (the total). But what if there is a car that is both white and has an auto. trans.? You would have subtracted it twice.

You need to use inclusion-exclusion.
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October 15th, 2010, 03:51 PM   #3
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Re: Probabilty

Hello, carter37!

Is there a typo?
The information is inconsistent .





Quote:



Try to sketch the Venn diagram . . .



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October 15th, 2010, 05:05 PM   #4
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Re: Probabilty

Soroban:

You are absolutely correct, the end should read "8 are white have an automatic transmission and a sunroof." Thanks for pointing that out.
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October 16th, 2010, 07:54 AM   #5
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Re: Probabilty

Hello, carter37!

Quote:
The end should read "8 are white, have an automatic transmission and a sunroof."

Ah, that clears it up!
And I was wrong about the 654 cars.




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[color=beige]. . . [/color]







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