Dice Rolling games in different scenarios

I interviewed in autumn 2021. Fairly standard probability questions. I didn't prepare, so I flunked the second round. See Mosteller's Fifty Challenging Problems in Probability with Solutions (you should be able to find a PDF online) for practice. My first-round interviewer was quite pleasant. However, my second-round interviewer arrived over five minutes late to the interviewer, sighed quite loudly when I was slower than he wanted and was overall quite rude. I was shocked by the lack of professionalism, and I even wish I had challenged him on it at the time. The interviewers can be quite poor at communicating (you can see this even in the example interview Jane Street have posted to their own website!) so make sure the question is completely clear to you before attempting to answer; don't assume anything. Lastly, if you come from a mathematical background, it'll often be tempting to try to find an exact solution. Jane Street isn't looking for this (again, see the example interview on their site). Focus on getting to a relatively quick answer that doesn't have to be too precise.