The **Probabilities**
worksheet computes and displays the *n*-step transition
matrix. The *Start* button sets the matrix to equal
the transition matrix defined on the Matrix worksheet.
The *More*
button, provides subsequent transition matrices.
The example below shows the transition matrix for the first
three months of the light bulb case. The 1-step
matrix is the transition matrix given in the original model.
The 2-step matrix is the square of the 1-step matrix. The
*k*+1 step matrix is produced by multiplying
the *k-*step transition
matrix by the 1-step transition matrix. The information
is colored green because it is computed by a VBA algorithm.

To illustrate the meaning
of the matrix contents, consider the 3-step matrix. An
entry in row *i* column *j* gives the probability
of a transition from state *i* to state *j* in
three steps. For example, the
row for 2-mo. gives the probability distribution for
the age of the bulb at some location, given that the
bulb was 2 months old at the location at the beginning
of a three month period.