Let X∼Geometric(p)X \sim \text{Geometric}(p)X∼Geometric(p) (number of trials until success). What is P(X>k)P(X > k)P(X>k)?
pkp^kpk
(1−p)k(1-p)^k(1−p)k
1−(1−p)k1 - (1-p)^k1−(1−p)k
kp(1−p)kp(1-p)kp(1−p)