Calculate the probability that at least 4 draws are required (until a diamond appears) both with and without replacement.
With Replacement:
$$1- ((1-13/52)^0(13/52) + (1-13/52)^1(13/52) +(1-13/52)^2(13/52))$$
Without Replacement: $$1-((13/52)+ (39/51)(13/51)+(39/52)(38/51)(13/50))$$
Is this correct?