You can model the probability for radioactive decay as a Poisson distribution. This is the probability for radioactive decay within a specific time interval. (I probably got some of it wrong here). P(k,μ)=λ^k⋅exp(-μ)/k! Is there a way to use this formula to derive the other formula for radioactive decay? N(t)=N0⋅exp(-λt) The only thing I've found, is all connected to differential equation, but nothing about how it is connected to Poisson distribution.