Marchov Chain question

Question

A Markov chain has the transition matrix shown below:

P= 0.3 0.2 0.5

0.7 0 0.3

1 0 0

If, on the first observation, the system is in state 2, what is the probability that on the next four observations it successively occupies states 3, 1, 2, and 1 (in that order)?

Answer 1

In a Markov chain, From is the row, To is the column; thus, p₂₃ = .3, p₃₁ = 1, p₁₂ = .2, and p₂₁ = .7, and the probability of completing these 4 steps in order is the product: .3 * 1 * .2 * .7 = .042