The next part would be a short excursion into conditional probability and into base law.

And we consider the following example, the following, let's call it, it's a fabrication

pipeline as a guiding example. And this fabrication pipeline is, well you have

some kind of machine and this machine outputs parts. So this machine

manufactures objects and let's say it manufactures balls, right, perfect circles.

So those come out of the machine and if they're good they're, you know, they're round

and symmetrical and perfect. But sometimes something goes wrong and you get, you know,

some kind of blob, right. So this is good, this is good, this is bad.

But the machine doesn't really know that something has gone wrong. It just fabricates things,

you know, this again is a good one, but we actually don't know whether this is, so

the machine can't tell properly manufactured objects from improperly manufactured objects.

So this is good, good and faulty and good. So what we need is, in this fabrication pipeline,

we need some kind of quality control. Let's say the quality control comes next. I'm going to

draw this as a large magnifying glass, which is

this. Could be what's happening here, right. So we have this magnifying glass and you can see that

an object is currently under, in this quality control. This also, let's say this quality

control is also a machine, so it's not a person doing this, it's also a machine. And depending on

what the quality control judges this object to be, this either goes into delivery.

So the, well, let's not call it delivery, let's call it okay. So if the quality control says that

it's okay, then, well, it gets delivered. So let's draw this as a box like this. Well, this is not

a nice box. So the object is in here and it will get shipped somewhere, right. If the quality

control says that this should be discarded, then it goes into the trash. So hopefully,

we have objects like these that go into the trash.

Right, like this. Okay, let's maybe draw another of those faulty objects. So,

right, so this is not a nice ball.

Okay, and maybe it's good to keep them visually apart. Right, so this is, this is red, this is not

good. Those go in here, and the green ones are the nice ones. They go into delivery. Okay, so

maybe this makes it more clear what's happening here. Okay, and we consider

the following events. Events are A, a given product

is good. Good means it's objectively good. It's a perfect circle, it's green. And A complement,

A complement AC means product is faulty. Faulty product. Again, this is objectively true. So this

is what we would know it to be if we have to, if we had perfect knowledge of the whole process.

And there is a related event, which, well, hopefully is strongly correlated to A itself.

Which is that quality control says that the object is okay for delivery. B complement would be that

quality control says that it is supposed to be discarded. So discard is

this, this pile here, the discard pile.

Okay, so I hope this fabrication pipeline makes sense to you. This machine autonomously pumps out

objects. Some are good, some are faulty. Then quality control looks at these objects. And

if quality control thinks that those objects are good, then it puts them on the okay pile.

If quality control thinks they're faulty, then these objects are faulty.

Then these objects go to the discard pile, which is the trash.

And let's say that by, well, let's say from experience, oops, from experience,

the probability that a given product is good, so that's the relative frequency of good products,

is 0.95, which is incidentally 19 out of 20. So 19 out of 20 objects are objectively good. So

this picture is a bit misleading right there.

They're not that many bad products in here. Most of them, 19 out of 20, are actually nice green round

circles. This means that in particular, that the probability that a given object is faulty is one

out of 20, which is 0.05.

Okay. And also, we assume that also from experience,

the probability that an objectively good product is labelled as faulty is one out of 20.