fugacity

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)

Happy they got the Taiwan part correct at least.

Having personally played Rocket League, (1800 hours), Valorant (500? hours), CSGO (2000 hours), League of Legends (2000? hours) and a variety of coop multiplayer games, I can tell you that the most toxic communities tend to be the competitive ones. Something about competitive games draws out the most hardcore crowd and that crowd tends to be a lot less friendly. Maybe it’s because people who play ranked games care about their ladder MMR, and the ones who are able to keep playing must have some kind of ego - you have to understand that a lot of people get fun out of winning, not from just participating in the game.

Regardless, the mechanism that rewards players is skill. And in these games, being polite, being nice to your teammates, none of it really matters if you aren’t skilled. Inherently there is a pecking order because higher ranked players are better than lower ranked players. Most games don’t reward direct toxicity of higher ranked players towards lower ranked players, but they don’t forbid it. Smurfing, for instance, allows a player to assert their superiority over lower skilled players. A carry on a team can be significantly more toxic towards their teammates since their teammates want the MMR from a win and will be willing to put up with being bullied or harassed. Just like another commenter mentioned, players compete against each other, and you will not really be friendly with your opponents in most ranked settings. But additionally, players also rely on their teammates. I think this is where a lot of the toxicity comes from.

When your friend dies to the enemy and gets t-bagged, your teammates aren’t pitying your friend for getting t-bagged. They’re mentally rolling their eyes that your friend was outplayed by their opponent and that’s why when you post on a forum the result is usually “git gud” and not “we should be more friendly”. I don’t think being toxic is positive to the health of a game. I could go into detail, but this post is already pretty long. But I want to point out, if the setting is a competitive game, merit is usually the driving factor regardless of toxicity or kindness. If you don’t gain that dopamine hit out of outsmarting or beating your opponents but rather simply from playing the game or socializing with other players, you probably should not bother touching these games - you aren’t the core audience for these games and you’ll find more enjoyment in other settings.

For the record, if you get t-bagged in a competitive game, the recourse is to either not look at the kill cam (CS:GO lets you turn it off), or try to improve so you don’t get t-bagged as often. Ragequitting, or going to complain that it should be turned off will get you nowhere. BMing your opponent is a popular thing in most competitive games, and it’s part of the reward for outplaying them. In many eyes, it’s not really all that different from a giant defeat screen when you lose. If you’re sensitive to this kind of stuff, I think you should find more friendly communities. Coop games generally tend to be better, as do more casual games, or FFXIV if you’re looking for an MMO. I would say most players (me included) consider the option to t-bag a feature and not a bug, because really the thing that upsets me the most is not getting t-bagged; it’s getting outplayed by my opponent so they’re able to do it in the first place.

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…