Probability, Probability Theory, Random Variable, Probability Distributions, Mathematics.
sum to 1, then the probability that the gun WILL NOT fire before or on the 9th pull is equal to 1 minus the probability that the gun WILL fire before the 9th pull. This is 1 — P(X<9) which comes out to ~0.23, so actually there is a 23% chance he will survive given 8 trigger pulls. X ~ NBin(r, p)