I interpret the question like this: suppose the sampling was purportedly carried out as if $363$ tickets of white paper were put in a jar, each labeled with the name of one person, and $232$ were taken out randomly after thoroughly stirring the jar's contents. Beforehand, $12$ of the tickets were colored red. What is the chance that exactly two of the selected tickets are red? What is the chance that at most two of the tickets are red?
An exact formula can be obtained, but we don't need to do that much theoretical work. Instead, we just track the chances as the tickets are pulled from the jar. At the time $m$ of them have been withdrawn, let the chance that exactly $i$ red tickets have been seen be written $p(i,m)$. To get started, note that $p(i,0)=0$ if $i\gt 0$ (you can't have any red tickets before you get started) and $p(0,0)=1$ (it's certain you have no red tickets at the outset). Now, on the most recent draw, either the ticket was red or it wasn't. In the first case, we previously had a chance $p(i-1,m-1)$ of seeing exactly $i-1$ red tickets. We then happened then to pull a red one from the remaining $363 - m + 1$ tickets, making it exactly $i$ red tickets so far. Because we assume all tickets have equal chances at every stage, our chance of drawing a red in this fashion was therefore $(12-i+1) / (363 - m + 1)$. In the other case, we had a chance $p(i,m-1)$ of obtaining exactly $i$ red tickets in the previous $m-1$ draws, and the chance of not adding another red ticket to the sample on the next draw was $(363 - m + 1 - 12 + i) / (363 - m + 1)$. Whence, using basic axioms of probability (to wit, chances of two mutually exclusive cases add and conditional chances multiply),
$$p(i,m) = \frac{p(i-1,m-1) (12-i+1) + p(i,m-1) (363 - m + 1 - 12 + i)}{363 - m + 1}.$$
We repeat this calculation recursively, laying out a triangular array of the values of $p(i,m)$ for $0\le i\le 12$ and $0 \le m \le 232$. After a little calculation we obtain $p(2,232) \approx 0.000849884$ and $p(0,232)+p(1,232)+p(2,232)\approx 0.000934314$, answering both versions of the question. These are small numbers: no matter how you look at it, they are pretty rare events (rarer than one in a thousand).
As a double-check, I performed this exercise with a computer 1,000,000 times. In 932 = 0.000932 of these experiments, 2 or fewer red tickets were observed. This is extremely close to the calculated result, because the sampling fluctuation in the expected value of 934.3 is about 30 (up or down). Here is how the simulation is done in R:
> population <- c(rep(1,12), rep(0, 363-12)) # 1 is a "red" indicator
> results <- replicate(10^6,
sum(sample(population, 232))) # Count the reds in 10^6 trials
> sum(results <= 2) # How many trials had 2 or fewer reds?
[1] 948
This time, because the experiments are random, the results changed a little: two or fewer red tickets were observed in 948 of the million trials. That still is consistent with the theoretical result.)
The conclusion is that it's highly unlikely that two or fewer of the 232 tickets will be red. If you indeed have a sample of 232 of 363 people, this result is a strong indication that the tickets-in-a-jar model is not a correct description of how the sample was obtained. Alternative explanations include (a) the red tickets were made more difficult to take from the jar (a "bias" against them) as well as (b) the tickets were colored after the sample was observed (post-hoc data snooping, which does not indicate any bias).
An example of explanation (b) in action would be a jury pool for a notorious murder trial. Suppose it included 363 people. Out of that pool, the court interviewed 232 of them. An ambitious newspaper reporter meticulously reviews the vitae of everyone in the pool and notices that 12 of the 363 were goldfish fanciers, but only two of them had been interviewed. Is the court biased against goldfish fanciers? Probably not.