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Simple Question - It's been a while since College

  1. Feb 27, 2007 #1
    I appreciate your help since I been out of college many years. I recently bought
    a 1980 Corvette, 4 Speed Transmission, Dark Blue Exterior, Oyster Leather Interior. GM will only give you the number made but not the combinations made.

    GM Stats On How Many Made:
    1980 Coupes made: 40614
    4 Speed Transmission: 5726
    Dark Blue Exterior: 4135
    Oyster Interior: 7104

    Could you give me the formula to work out how many were made with my combination. Also is this called a 'Joint Distribution'. Like I said it's been a long time.

    I appreciate your help.

    Blue Vette
     
  2. jcsd
  3. Feb 28, 2007 #2
    http://en.wikipedia.org/wiki/Inclusion_exclusion_principle

    Where the cardinality of the union is precisely 40614, and then you just apply the formula.

    Reply back if you need help.

    Whoops, You're not given enough information. I figured this was a homework question so they would've given you all the necessary information.

    I wonder if we could put some bounds on that though...I'm not much of a discrete person so I'm not entirely sure.
     
    Last edited: Feb 28, 2007
  4. Feb 28, 2007 #3
    Since the stats only state how many Coupes had the above characteristics individualy but not in combination, there is no way to work these stats to say how many cars had each of the above characteristics. Mathematically it is possible that all cars with a dark blue exterior had each of the other characteristics, but it is also mathematically possible that no car had each of the above characteristics. Thus the answer to your question is somewhere between 1 and 4135 since we know of your car!
     
    Last edited: Feb 28, 2007
  5. Feb 28, 2007 #4
    ZioX - Thanks for trying to help me with my general question. I'm not sure what bounds you need. Also could you insert the numbers into the formula as I'm not sure where to align them..

    Thanks
     
  6. Mar 2, 2007 #5
    Ramsey2879 - Thank you for your response I really appreciate your help.

    My Corvette black book does have a lot of information. If I give you more information related to my question for that year and car (Dark Blue, 4 speed Manual, Oyster Leather) would that help any. They offered a total of 5 colors including my Oyster color with Dark Blue as listed below. I hope this narrows it down and maybe you can give me an approximate number made of my combination alowing for some margin of error.

    If you can work it out can you write the formula so I can use it on other cars.

    EXTERIOR COLORS & ........INTERIOR COLORS
    NUMBER MADE:................OFFERED WITH EXTERIOR COLOR:
    Dark Blue.......4,135..........Bk-Db-Ds-O-R
    White...........7,780...........Bk-Cl-Db-Ds-O-R
    Silver...........4,341...........Bk-Cl-Db-O-R
    Black...........7,250...........Bk-Ds-O-R
    Dark Brown...2,300...........Bk-Ds-O
    Yellow.........2,077...........Bk-O
    Dark Green......496...........Bk-Ds-O
    Frost Beige...3,070...........Bk-Cl-Db-Ds-R
    Dark Claret...3,451...........Bk-Cl-Ds-O
    Red...........5,714.............Bk-Ds-O-R
    Total 40614

    INTERIOR COLOR QUANTITIES:
    Black (Bk).......... 6,776
    Claret (Cl)...........4,974
    Dark Blue (Db).....3,842
    DoeSkin (Ds).......8,926
    Oyster (O)..........8,912
    - Cloth 1,808
    - Leather 7,104
    Red (R)..............7,184
    Total 40,614

    Transmissions made:
    4 speed Manual .......5,726
    Automatic .............34,888
    Total 40,614


    GM Stats On How Many Made:
    1980 Coupes made: 40614
    4 Speed Transmission: 5726
    Dark Blue Exterior: 4135
    Oyster Interior: 7104
     
    Last edited: Mar 2, 2007
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