Radioactive Emission 

Particles are emitted by a radioactive source according to a Poisson process at the rate of per hour. Find the probability that no particle is emitted during at least one of five consecutive hours.

In[1]:=

X emissionProcess = PoissonProcess[Log[5]];

In[2]:=

X ListLinePlot[RandomFunction[emissionProcess, {0, 10}], InterpolationOrder -> 0, Filling -> Axis]

Out[2]=

Probability of no emission during at least one of five consecutive hours.

In[3]:=

X 1 - NProbability[x[1] > 0, x \[Distributed] emissionProcess]^5

Out[3]=