alt Hacker NewsI thought I'd look this up. If you've had 9 successful attempts, assuming nothing has changed between them and no other prior knowledge about success probability, then Laplace’s Rule of Succession says the probability of the next mission being a success is about 83.3%, i.e. there is a 1 in 6 chance of failing next time.
> and no other prior knowledge about success probability
This phrase is misleading, as Laplace's Rule of Succession is equivalent to assuming a uniform Bayesian prior over all values of p. That is, before any experiments, a 50% chance of success. Depending on the situation, this may be roughly accurate or wildly wrong. You cannot appeal to this rule to resolve the situation.