I'd recommend using the beta distribution. I'd recommend Jeffrey's prior (beta(1/2,1/2)), though I don't fully understand it.
I've only ever used it to figure out the probability of getting heads on the next step, but you could just multiply these together to get the probability of the sequence, so it's 0.5/1x1.5/2x2.5/3x3.5/4x4.5/5x4.5/6x4.5/7 if that is where the bug is (since it failed five times then passed twice, or might as well have since order doesn't really matter, and clearly it will pass the next ten) and 0.5/1x1.5/2x2.5/3x3.5/4x4.5/5x4.5/6x4.5/7x5.5/8x6.5/9x...x14.5/17 if you didn't find it. The first seven terms will cancel, so you just get that it's 5.5/8x...x14.5/17 = (14.5!/4.5!)/(17!/7!) = 0.0906 times as unlikely if there's no bug.
I'm afraid I don't quite see how to apply this to the problem. The beta distribution is presumably a probability, but what is it a probability of? Is there an interpretation to its two parameters that I'm not seeing?
I have successfully confused myself about probability again.
I am debugging an intermittent crash; it doesn't happen every time I run the program. After much confusion I believe I have traced the problem to a specific line (activating my debug logger, as it happens; irony...) I have tested my program with and without this line commented out. I find that, when the line is active, I get two crashes on seven runs. Without the line, I get no crashes on ten runs. Intuitively this seems like evidence in favour of the hypothesis that the line is causing the crash. But I'm confused on how to set up the equations. Do I need a probability distribution over crash frequencies? That was the solution the last time I was confused over Bayes, but I don't understand what it means to say "The probability of having the line, given crash frequency f", which it seems I need to know to calculate a new probability distribution.
I'm going to go with my intuition and code on the assumption that the debug logger should be activated much later in the program to avoid a race condition, but I'd like to understand this math.