You can answer that question for each prior. The probability of, say, 3 failures is the sum over all priors of the probability that that prior is true, times the probability that it would leave you with 3 failures.
I leave writing a program to calculate this as an exercise to the reader. I've put enough time in on this one already, I have paying work to get back to.
You can answer that question for each prior. The probability of, say, 3 failures is the sum over all priors of the probability that that prior is true, times the probability that it would leave you with 3 failures.
I leave writing a program to calculate this as an exercise to the reader. I've put enough time in on this one already, I have paying work to get back to.