In the experiment of drawing balls from bag. Does 3 in $X_i \sim \mathit{Binomial}(3, \theta)$ mean there are 3 balls in the bag? I'm learning a statistics tutorial which considers
$$
X_i \sim \mathit{Bernoulli}\left(\frac{\theta}{3}\right)
$$
to describe an experiment where one draws a ball 4 times with replacement from a bag that contains 3 balls.
And then the tutorial gives another experiment where
$$
X_i \sim \mathit{Binomial}(3, \theta)
$$
and $(x_1,x_2,x_3,x_4)=(1,3,2,2)$.
I understand
$X_i \sim \mathit{Binomial}(3, \theta)$
when considering 3 the number of experiments where one experiment/trial flips one coin one time and $\theta$ denotes the success possibility for each trial. but I don't understand the definition of one experiment in that tutorial.
Could someone give me a hint?
Possible setting 1
Does 3 in $X_i \sim \mathit{Binomial}(3, \theta)$ mean there are 3 balls in the bag?
Note that in the second experiment, 3 blue balls are observed which means there already are 3 blue balls in the bag, which means, all 3 balls are blue, if the 3 in $X_i \sim \mathit{Binomial}(3, \theta)$ means there are 3 balls in the bag.
Alternatively, the experiments are using different bags, but that doesn't seem to be compatible with the definition of binomial distribution.
Possible setting 2
Does it make sense to define one experiment as follows?
"draw a ball, record if it's blue, and put it back in the bag, repeat 4 times"
In other words, one experiment draws 4 times, so the possible outcomes are ${0, 1, 2, 3, 4}$.  And then, $X_i \sim \mathit{Binomial}(3,\theta)$ means doing the experiment 3 times.
In this setting, $\theta$ doesn't mean the possibility that one blue ball is observed, so what does $\theta$ mean?
Possible setting 3
Another possible definition of one experiment could be
"draw 3 balls from the bag, record how many blue balls observed, and then put the balls back in the bag"
So the possible outcome of one experiment could be ${0, 1, 2, 3}$. See the difference between this setting and setting_1?
The 3 in $X_i \sim \mathit{Binomial}(3, \theta)$ means doing the experiment 3 times.
Again, what does $\theta$ mean in this setting?

The parameters of the binomial distribution are n, the number of independent trials and p, the probability of success on each trial.
So here, the three in the second experiment means that three balls will be drawn from the bag. In this setup, they must be drawn with replacement, because otherwise the success probability would change each time and the binomial distribution would be inappropriate.
I'll have to assume that drawing a blue ball counts as a "success" here. I would say there must be more than three blue balls in the second experiment, because in the first result, x1 is 1. This means at least 2 non-blue balls were drawn.
