fugacity

An unfinished civil war in which the Republic of China lives on in a tiny island? Damn, must have been a real stalemate for the KMT and Communist Party.

For the record, I absolutely believe China would attack Taiwan, when they think they are ready. And you don’t have to take my word for it: what of all those missiles Taiwan posseses? Are they pointed towards or away from the strait?

As for being left alone, the only reason Taiwan can live in peace and prosperity is because of its strategic semiconductor fabs and the publicity it generates. Yes, the publicity it generates puts us the forefront of global conversations and keeps Taiwan safe.

Now, if you really are Taiwanese, if China and Taiwan are one, do you really think China would let TSMC do as they please and not immediately takeover the company for SMIC? Or do you not remember what happened to Jack Ma? You think Taiwan can vote how it wants while still being part of China? Taiwan is part of China just as much as Ukraine is part of Russia.

By the way, last I checked in December when I visited my parents, rubber ducks and Winnie the Pooh aren’t banned in Taiwan. I wonder about Hong Kong and its one country two systems ;)

Lmao no that’s not the status quo of Taiwan. Or maybe I should ask you what happened to Hong Kong?

his edit does not assume that; it’s the cleanest way of doing the problem

P(failure second try)=(2/3)^2 since you can eliminate one choice but 2 others are still wrong.

To total:
P(failure)=(3/4)^2*(2/3)2=1/4
1-1/4=0.75

So the probability of passing is 0.75

Edit:
Remark: this problem is elegant if you attempt to calculate the passing as the complement of failure rather than enumerate all successes. Shouldn’t take more than 3 minutes with a clear head if you know the correct approach. If this was an college level intro probability exam question, it should be done the fast way since it’s meant to eat up your time otherwise.

P(passing) = 1- P(failure)
P(failure) = P(failure first try)*P(failure second try)
P(failure first try)=(3/4)^2
P(failure second try)=(gonna post in reply)

Not that this comment is all that relevant to you, but here’s a wall of text for context:

The devil is probably in the details here. My assumption is that your denatured alcohol is referring to ethanol mixed with other toxic alcohols (such as methanol).

This can’t be 100% pure ethanol because it MUST contain denaturants to discourage drinking, otherwise it would not be denatured and would legally require an additional excise tax. In that case, you might find it as Everclear (190 proof or 95% or ethanol by volume at highest concentration). It can be close to 100% alcohol, of course, because methanol is an alcohol.

I HAVE seen (at least in the US) food grade USP purity ethanol for sale (with additional cost due to excise tax inclusion) that’s at least 99.5% pure. I have also seen 99% purity isopropyl alcohol (IPA). My point in the reply to the original content is that it’s not accurate. Distillation of binary mixtures results in azeotropes that prevent purity of more than 91% IPA (by volume) and ~95% ethanol. But there’s ways around it such as adding a third solvent for a ternary mixture, salting out (shown in some chemistry demonstrations), changing the pressure of distillation, or using molecular sieves to remove water content. Alternatively, you could use freeze distillation, or even zone melting if you chose to freeze the mixture instead of boiling it. In fact, once you PASS the azeotrope, you can actually distill at standard pressure albeit what you want and don’t want in the column would switch places.

Getting the last few percent of water out of it definitely costs more, but it’s not something so hard that you can’t find commercially available alcohol solvents at purities above the azeotropic point. I know this is the case since I’ve acquired them for home use and have used them in multiple lab settings before. The annoying part for those who REALLY don’t want much water in the solvents is that at that point your solvents are hygroscopic and unless sealed properly or kept in a desiccated environment they’re gonna tend to absorb water back toward the azeotropic point.

Ethanol is similar to IPA in solvent properties but they won’t be the same. I don’t have enough wet lab experience to give a good answer in this regard though. If you’re able to take things apart, I’ve cleaned PCBs the Louis Rossmann way, which is with Branson EC solution and sonication. Drying is really the most important step there ;)

That’s mostly correct but I don’t think it’s entirely accurate. Distillation is useless at the azeotropic point but ternary mixtures are used to break the azeotrope. Once you move past the azeotrope you can continue distillation to high purity. You could also do pressure swing distillation but my guess (even though I’m not exactly a chemical engineer doing unit operations for a living) is that it wouldn’t be economical. Of course, getting “100%” pure anything is really a different story…