False discovery and multiple test

#1
I'm reading about the familywise error rate here and trying to put it into perspective. According to this, we calculate FWER = 1 - (1 - alpha)^n. In their example n=10, and with alpha .05, they say this gives 40.1% chance of a type 1 error. Is this practically saying that if i run a study and make 10 comparisons, the probability that an significant result (if one is observed!) is false is 40%? In other words, given that I see any significant, there is a 40% chance that this is false.? So what if I see 4 significant here? It's says approximately ~1.6 of those is false? I think i am right but want to be sure.
 

Dason

Ambassador to the humans
#2
What it's saying is that even if all of the tests are such that the null hypothesis is actually true that there is a 40% that you will get at least one test coming out as significant. It doesn't say anything about the probability that a discovery is actually false or true or anything like that. Just that if all the tests are actually null we still have a 40% to get at least one significant result.
 
#3
What it's saying is that even if all of the tests are such that the null hypothesis is actually true that there is a 40% that you will get at least one test coming out as significant. It doesn't say anything about the probability that a discovery is actually false or true or anything like that. Just that if all the tests are actually null we still have a 40% to get at least one significant result.
I see, so it is more something you say prior to running the testing?

But then I'm having some problem understanding how we might interpret the situation when we do observe (e.g. 4) significant results. What would be the interpretation in that case?