A Markov chain is a graph model that describes the probabilities of a system

transitioning through a sequence of possible states. Each edge is labelled with

a probability. The probability of the system transitioning to a given state is

dependant only on the current state. For example, in the Markov chain shown

below, if we start in state $A,$ there is a $50\%$ probability of transitioning to state

B$.$

We will say the system generates the sequence $A,B,C$ if it starts in $A,$

transitions to $B$ and then transitions to $C.$ Assume the system always starts in

state A$.$ What is the probability of the system generating:

The sequence $A,B,C[1]$