>What are the odds that everyone in your interview is dumb/inexperienced/busy or an asshole versus the odds that it's just you?

Let's assume that your interviewer is selected at random from the population and that traits are independent from each other. Let's further assume that 50% of people are 'dumb', that 30% of people are inexperienced, that 90% of people are 'busy', and that 50% of people are assholes. Honestly, I think these estimates are kind to most people in corporate America, but we're going from a random sample of the population. You can play around with the odds yourself and see what you get.

Now, my probability math isn't the best these days, but I can give this a go:

The odds that your interviewer is all four of the listed traits is ~7%.

Writing out the matrix for all the probabilities is going to take a while and really isn't formatted well for HN, so I'll skip most of them and just focus on the dumb assholes. So the odds that your interviewer is:

- dumb, inexperienced, and an asshole is ~8%

- dumb, 'busy', and an asshole is ~23%

- dumb and an asshole is ~25%

Now, that's just a single interviewer. You typically get a few rounds of them. Let's say that we have three interviewers to go through. What are the odds that at least one of them is a dumb asshole? Well, again, my probability math isn't the best, but I think that you just add the events together. So, the odds that you have at least one dumb asshole to be interviewed by is ~75%. Again, though, probability math is a head-trip to me and I always have to relearn it when I do it.

Now, you asked what the odds were that the person being interviewed is the one at fault. Again, we have to assume that we are being picked at random from the population. I'll use the numbers as above and assume they are randomly distributed in a person likewise.

The odds that both you are all four things (dumb/inexperienced/busy/asshole) is still just ~7%, and likewise for the rest of the permutations. For the sake of brevity, let's assume that the interviewee is dumb asshole and that the person giving the interview is NOT a dumb asshole. The probability that they are not a dumb asshole is ~75%. The odds that you, the interviewee, are a dumb asshole are ~25%. Again, though, probability math is a head-trip, I think the odds are then just multiplied to give the odds of that particular interaction at ~19%, or just shy of 1/5th of the interviews.

Now, again, you have to go through three of these rounds of interviews, each time going through the independent probability math. Again, my probabilty math isn't the best here, but I think the odds that you are a dumb asshole and that the interviewers are NOT dumb assholes is ~56%. Again, assume random distributions of traits and random sampling of people and that my distributions of traits are accurate.

Hope it helps!

EDIT: Crap! You asked a question I did not answer (sorry): what are the odds that ALL the interviewers have NONE of the four listed traits and you have at least one of the traits. Well, the odds that a random person does NOT have ANY of the listed independent traits is ~2%. That ALL three of these hypothetical interviewers would not have ANY of the listed traits is ~0.000054%. Now, that you have NONE of the traits is ~93%, but lest focus on the dumb assholes again. So the odds that you have at least the dumb trait OR the asshole trait are ~50% ( Thank God I chose both those percentages to be the same!). So, given that you have at least one trait, and that the interviewers have NONE of the traits, what are those odds? They are ~0.000027%. Again, though, my math is not always the best, so please re-check.