See subject. It’s in my mind whenever I do a bird. And then it hit me: it’s a Straight Dope question!
The query could apply to the full set of three giblets or any of its subsets.
What are the necessary data?
I don’t know how chicken processors do the eviscerate-separate-package-restuff procedure. It’s probably interesting.
Astounding question. I’ve made 50 trips around the Sun, and never once in my entire life did it ever occur to me that the dog and I are dining on two separate birds. But when I think about it, that must of course be the case. They must be separated, packaged, and reinserted into another chicken.
I have seen chickens with extra giblets in them, such as two hearts or livers, so I’d say that they may not always come from the same bird, depending also on how they process them (which may be different among processors), and here is an article about a lawsuit concerning extra giblets (really).
The relevant fact is that you only get giblets with a whole chicken, yet most people buy parts. Oh sure, in some stores you might see a package of chicken livers or gizzards, but still, most people just buy parts. So the remainder must be considered “chicken by-products,” and used in things like pet food. What this probably means is that it’s pointless to keep a chicken’s giblets with the chicken, when you don’t even know whether the particular chicken will be sold whole, with its giblets, or in parts, without. The only sensible thing would be to remove them from all chickens. Then, it’s no problem for someone to just grab a handful of giblets for packaging.
The giblets are not set aside to be returned to the same chicken. I was dumbfounded when I found out, too.
So, the answer is no. of chickens per processing batch x no. of giblets per chicken.
Once upon a time I processed whole chickens for pay. (for about two weeks, between college terms) It was a small processing line and the parts were returned to the same chicken because, well, that was the simplest and most efficient way to do it.
There are huge plants that process tens of thousands of birds per day and they may be different, but where I worked the innards went back into the chicken from whence they came.
I’ve observed this too - also, cases where parts you’d expect are missing. I’m not sure why, but my wife and I always get a chuckle when we find a heartless chicken. 
Plants have become larger over the years but if a plant processes, say 76,000 birds per day for an eight-hour shift, the odds are about 1 in 65,000. The odds are less than the total kill as some gibbets may be damaged in processing and disposed of.
Each bird is eviscerated, that is the guts are pulled out of the bird and eventually removed. Some plants do not process the giblets but dispose of them. Others process them. The gizzard which is something like a muscular stomach has a tough skin that must be removed by a wicked looking machine that sometimes removes fingers, too.
One method of processing is that these giblets run to another machine that puts a few in a bag. The bag is then carried by a special line which goes to the bird and inserts it. I believe this is done when the bird is packaged.
BTW, the same is true for chicken that is cut up. It is very, very, very unlikely that when purchasing a cut up chicken that the parts all came from the same bird.
As per another recent thread, “whenever I do a bird” would have a quite different meaning in the U.K. 
Chickens have politicians? Who knew…
Lawyers. The brainless ones are the politicians.
I buy a lot of whole chickens. 80% of my fryers have no giblets, while 100% of the roasters have giblets. 90% of the roasters have a complete set with no extras or shorts, while the few fryers that I find with giblets actually have a warning on the label that states the giblets may or may not be missing parts.
I would say it is very safe to say, when buying from a large chainstore, that the giblets were removed, stuffed into sets in to the little paper sacks, and reinserted down the line, with no regard to reuniting the bird with its giblets. I don’t eat the gizzard, and I love chicken liver. I’d put the heart into gravy, if I was making giblet gravy. I think a lot of Americans wouldn’t fool with the giblets, so the processor retains them on many birds in order to make an extra dollar through another sale.
When the giblets go to the station where a few of them are picked, is that done by machine? Usually it’s the anatomically correct complement, but how do the multi-organs occur?
“Goes to the bird” means goes to that bird? That would imply extraordinary time/process matching.
Basically you’re saying that the odds are vanishingly small, as some of the hard-core types here like to put it. But there has to be some way of figuring them out, based on some critical numerical assumptions. I need help from statistics people.
Are their any pertinent data I could Perdue might supply me? I’ll do the email.
They’ve gotta maintain those gibbets. That’s exactly why they’re getting lower yields. The birds have to know what happens if they don’t cooperate. And if they do cooperate, I guess.
I totally suck at math, especially statistics, but I’ve found the best way to get an answer around here is to do it wrong so people who know more come in to correct you.
So I’m gonna go with the multiplication method. If there are 76,000 processed in a day, then my odds of getting one is 1. If there are 76,000 hearts removed in a day, then my odds of getting a particular one (the one that matches my chicken) is 1:76,000. So if I want to know what my odds are of getting a particular chicken and the heart that came out of it and the liver that came out of it after they are separated and stuffed at random, it’d be 1: (76,000)(76,000), or 1: 5,776,000,000. For each additional giblet, multiply again.
Again, this is probably all wrong, but if I post it, some statistics person out there will be jumping out of her skin until she corrects it, and then we’ll know. 
(I’ve also found the best way to clean my house is to invite a friend with OCD over, feed her some wine, and start cleaning poorly in front of her. 
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