Simple Question - It's been a while since College

• Blue Vette
In summary, the conversation is about a person who recently bought a 1980 Corvette with specific characteristics such as a 4 speed transmission, dark blue exterior, and oyster leather interior. They are trying to figure out how many cars were made with this specific combination, but the GM stats only provide information on how many cars had each characteristic individually, not in combination. The person is asking for a formula to calculate this information and is wondering if it is called a 'Joint Distribution'. There is a discussion about putting bounds on the calculation and narrowing it down with more information, such as the total number of cars made with each exterior and interior color.

Blue Vette

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:
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.

Blue Vette

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.

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Blue Vette said:
GM Stats On How Many Made:
4 Speed Transmissions: 5726
Dark Blue Exterior: 4135
Oyster Interior: 7104

Blue Vette
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!

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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

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
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

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

GM Stats On How Many Made: