Let's say that I have a single six-sided die, which I suspect might be weighted or rigged somehow to always give a six. Let's also assume that the only way I have to determine whether it is actually rigged is by rolling it (admittedly, in real life, I may be able to tell from holding it). I roll it several times in a row and it always gives a six. Do some math to determine:
a. Using a "frequentist" approach, how many sixes in a row would I need to see before I was 95% sure that what I was seeing was a series of sixes (and not just random chance)?
b. Using a Bayesian approach, how many sixes in a row would I need to see before I was 95% sure that what I was seeing was a series of sixes (and not just random chance), given that my prior expectation that the die was weighted is 10%?