2.3, 3.5 Due on 4/1/2008

Difficult:

In the solution of the example in section 3.5, I think I understand the wording of the solution.  However, I have problems understanding the difference equation which is

a(n+1, k)=a(n, k)+a(n, k-1)

Why isn't the difference equation as the one showed below?

a(n+1, k)=a(n+1, 1)+a(n, k-1)

Reflective:

Reading Theorem 1 in section 2.3 helps me remember how to do the proofs by induction.  Also, by reading the problem in section 2.3, I learned how conditional probability theory can be applied in the practical world.