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October 15th, 2010, 10:46 AM  #1 
Newbie Joined: Oct 2010 Posts: 4 Thanks: 0  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? 4102633867= 42? 2. How many are white, have an auto. transmission and don't have a sunroof? 348=26? These answers seem entirely too simple to me. Any help would be greatly appreciated. 
October 15th, 2010, 11:40 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  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 inclusionexclusion. 
October 15th, 2010, 03:51 PM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Probabilty Hello, carter37! Is there a typo? The information is inconsistent . Quote:
Try to sketch the Venn diagram . . . [color=beige]. . [/color]  
October 15th, 2010, 05:05 PM  #4 
Newbie Joined: Oct 2010 Posts: 4 Thanks: 0  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. 
October 16th, 2010, 07:54 AM  #5  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Probabilty Hello, carter37! Quote:
Ah, that clears it up! And I was wrong about the 654 cars. [color=beige]. . . . . . . . . . . . . [/color] [color=beige]. . . [/color]  

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