Geometric is similar to binomial, except that now the variable of interest is the number of trials required to reach the first success, when before we were counting how many successes there were in so many trials. Thus, the conditions for the geometric setting are different. First, each observation is either success or failure. Second, the probability of success for each observation is the same. Also, all observations are independant.
Now, the formulas. The geometric probability that X takes any value is
P(X = n) = p(1-p)^(n-1)
The mean of X is 1/p, and the probability that it takes more than n to see the first success is P(X > n) = (1-p)^n
