In a society of population N, the probability is p that a person has a certain rare disease independently of others. Let X be the number of people who should be tested until a person with the disease...

In a society of population N, the probability is p that a person has a certain rare disease independently of others. Let X be the number of people who should be tested until a person with the disease is found, X = 0 if no one with the disease is found. What are the possible values of X? Determine the probabilities associated with these values.