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)

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…