What personality traits could I expect from a Labrador Retriever and Black and Tan Coon hound mix.?

whatever you see from the dog.
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Because of the hound, I'd say there may be trouble training the dog to come on command every time, and to rely on his behavior off leash.
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like humans it depends on which parent was what species, But labs are hyper and super loyal, black and tans are usually smart as hell and over protective yet calm , so I think they balance out to a good smart loyal dog, But black and tans are very common to parvo and puppy diseases, specially the mixed black and tans so make sure puppy shots get done swiftly, good luck
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There is no way to tell.
It could go either way really. Not all the puppies will be the same, some will take after one breed while the others take after another.

One breed does not "balance out" the other.
It's also unclear as to whether or not this dog will be hard to train off leash due to the hound mix because again, it's impossible to determine which breed the dog will represent - there's even a chance the dog can represent a little from both.

This is also assuming that both dogs were purebred to begin with - if not, it will be even harder to determine.
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http://www.dogbreedinfo.com/labrador.htm

http://www.dogbreedinfo.com/blackandtancoonhound.htm

Read about the temperaments and problems both breeds are prone to. Without a genetic test done on both parents to determine what genetic diseases, if any, they are carrying, you have to assume your dog might inherit any genetic defects either breed is prone to, and they may express themselves mildly or severely.

As for personality, read the personalities of both dogs. If you don't like the personality traits of either breed, do not get a mix of either breed as your dog has a random chance of inheriting any or all of them.
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A retriever that sniffs a lot.
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Can't tell, it could have some traits from a lab and some a lab doesn't have same with the hound. Just look up both breeds and you can pick up if you dog shows any. But since its a mutt you never really know what you're getting.
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