Understanding R's Definition In R, 

the syntax for the geometric cumulative distribution function is 
  * ''pgeom(q, prob, lower.tail = TRUE)'' 
  * q : The number of failures before the first success occurs.
  * prob : The probability of success in a single trial $(p)$.
  * lower.tail = TRUE (default) : Calculates the probability of experiencing q or fewer failures before the first success, i.e., P(X <_ q) where X is the number of failures. 
    * This means: Success on the 1st trial = 0 failures (q=0)
    * Success on the 2nd trial = 1 failure (q=1)
    * Success on the 3rd trial = 2 failures (q=2)