The apparent paradox of exponentially distributed inter-earthquake intervals

On a global scale, large earthquakes are Poisson-distributed in time which implies that the inter-earthquake intervals are exponentially distributed. Thus, a simple-minded estimation of the most probable interval could conclude that the most probable occurrence time for a large earthquake would be now! This thesis is unsupported by observations. The apparent paradox is explained when characteristics of the interval cumulative distributions are explored for different seismicity rates.