Probability of radioactive isotope survival and lifetime

Based on wikipedia,  particle decays is a Poisson process.  The probability that a particle survives for time t before decaying is the Poisson waiting time, i.e., an exponential distribution.  This is amazingly similar to the coalescence simulation in population genetics.

where tau is the mean lifetime of the particle and gamma is the Lorentz factor of the particle. This is basically the first order reaction.