If I get to pick which eggs I crack I could probably open a hundred. I grew up on a chicken farm, so I know them when I see them. When we had a young flock I could have gone through the chicken house and grabbed several.
Are you just going by size, or is there some other criterion? My mom’s hens have been known to lay single-yolk eggs as large as four ounces (and yes, they were chicken, not geese, and no, I have no idea how they managed that).
The shape is often different from single yolk eggs; I’m sure I’d miss some double yolk eggs that aren’t misshapen at all, but the vast majority of large slightly misshapen eggs I’ve seen in my life have been double yolks.
This. In a carton of Jumbos, an odd shaped egg is more likely to be a double you’ll.
This is the first misunderstanding. This statement is effectively that if I take any 3 eggs then all three will be double-yolked. Since the number of eggs is finite then that means ALL eggs are double-yolked.
The best that I can gather about your OP is that you think that egg double-yolkness is not independent. Otherwise p(3 DYs in a row) does equal (1/1000)^3. So if not independent then it is conditional (eliminating being exclusive for obvious reasons) so yes Bayesian may apply here. But help me out here: what is the condition? Anyone here please tell me what the A and B are for the OP’s idea of looking for p(A | B). @Ynnad you hint at jumbo eggs but immediately talk about all eggs.
All this being said is that the process the OP describes has nothing to do with Bayesian probability. Bayesian probability would be something like if we know p(double-yolk given a jumbo egg) then what is p(a jumbo egg given double yolk). Is that where you are going with this OP?
I would highly advise the OP to watch this video by Veritasium discussing Bayes Theorem, real-life and updating ideas. I’m pretty sure it explains a lot of the concept you are trying to work out through this thread.
and then Saint_Cad said, “This statement is effectively that if I take any 3 eggs then all three will be double-yolked”
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I thought it would be obvious that I meant only those three particular eggs that I had already cracked. We now know for certain that those three particular eggs had double yolks. I did not mean for the statement to somehow imply that all eggs in the universe must have double yolks just because of the double yolks in those three eggs. That would be absurd.
And that is the problem with your OP. It lacks preciseness so what you are saying mathematically and what you mean are two different things. That’s why I’m asking what you really mean and what does Bayesian probability have to do with it. For example, you talked about the probability of three eggs in a row having double yolks is 100% which as you point out is absurd. I believe you meant that the probability of there being an event (aka at least one) wherein there were three double yolks in a row is 100% is true but how useful is that. It’s basically just saying what happened happened.
And again, what is your conditional? Bayesian probability deals with this happened given that that happened or in other words two variables related to each other. One is obviously the double yolks but what is your second variable? Jumbo size? Eggs from the same vendor? The same farm? That is why I’m saying this is not a Bayes Probability problem. If you are assuming non-independence (and I’m not sure why you dismiss that) then it is a Poisson Distribution problem. And the answer to your question is simple. A Poisson distribution depends on the average number of events so in this case 1 out of every 1000 eggs. As you gather more information that average can change and thus your distribution will change slightly.
Yes, it means exactly that and it is a fairly useless statement as far as this discussion goes. However, I through it in there anyway because (in my mind at least), it doesn’t make much sense to talk about the probability of an event when that event has already occurred.
Also, please note that in my OP I did not ask “How do we apply Bayes’ Theorem?” Instead, I asked “[C]an we apply Bayes’ Theorem … ?”
Nope. You should watch that Veritasium video I linked to.