If a coin that comes up heads with probability is tossed repeatedly, the toss on which the first head is observed follows a geometric probability distribution. Drag the sliders and watch how the distribution changes. The mean of the distribution—the toss number on which one "expects" to observe the first head—is marked with a red circle on the horizontal axis.

The Mathematica built-in function GeometricDistribution is for the number of failures before a success, so there is a shift by 1 from that geometric distribution to the distribution shown here.