So thinking about this some more: we're assuming engines have some "true failure rate" which we're trying to divine from evidence. 2% is currently the mean of your distribution on TFR, but the relevant question is what's the variance of your distribution?
Uniform prior, updated on the evidence that 1/36 engines have failed, I think this gives P(TFR = x) = x(1-x)^35 / (int x(1-x)^35 dx from 0 to 1). Apparently the integral is 1/1332, so P(TFR=x) = 1332·x·(1-x)^35. But that seems to have a mean of 5%, compared to your value of 2%, so I may have done something dumb?
Uniform prior, updated on the evidence that 1/36 engines have failed, I think this gives P(TFR = x) = x(1-x)^35 / (int x(1-x)^35 dx from 0 to 1). Apparently the integral is 1/1332, so P(TFR=x) = 1332·x·(1-x)^35. But that seems to have a mean of 5%, compared to your value of 2%, so I may have done something dumb?