A diagnostic test is applied to determine the status of a component which is known to be in one of two states (state 1 and state 2). Let a denote the probability that the test indicates that the component is in state 1. The diagnostic test is applied repeatedly until a stopping condition is satisfied. Let $Y_{1}(t)$ denote the number of the first applications of the test that indicate that the component is in state 1, and let $Y_{2}(t)$ denote the number of the first applications of the test that indicate that the component is in state 2,t=1,2,... . The applications of the diagnostic test terminate when $Y_{1}(t)-Y_{2}(t)=q$
where q is some positive integer. Model the application of the diagnostic test using a discrete-time Markov chain.
Can someone explain to me how to model this problem as Markov chain.
Thanks