Assume the number of radioactive nucleus is N(t) --- not yet decayed into daugheter product.
Each nucleus has the same probability p (p<1) decayed into daughter product.
It means that dN(t)/dt= -p*N(t) , where dN(t) is the number of nucleus decayed into daughter product at time t.
The solution is N(t)=N(0) e [sup]-pt[/sup], where N(0) is total number of nucleus at time t.
Each box represent a nucleus.
This applet let you set the probability for a nucleus to decay and watch how the number of decayed nuclei (color changed to RED) increased with time t.