State Transition Probability Interview Questions
How to solve state transition probability interview questions with state choice, transition probabilities, absorbing states, and expected values.
Candidates learning recursive, Markov-style, and pattern probability setups.
Choose useful states
A state should make the next-step probabilities clear. For random walks, position is often enough. For pattern waiting, partial matched pattern may be the right state.
Write transition probabilities
For every state, list where the process can go next. If probabilities from a state do not sum to one, the model is incomplete.
Add absorbing states
If the process can end, include a done or boundary state. Boundary values usually anchor the recurrence and prevent circular ambiguity.
Concrete example
For a game where a score moves up with probability p and down with probability 1 - p until hitting a boundary, the state is score and transitions are score + 1 and score - 1.
Probability versus expectation
Use the same transition graph for hitting probability or expected time, but write different equations. Expected time has a step cost; hitting probability does not.
Common mistakes
Candidates often choose states based on the story rather than the future. Ask: if I know only this state, can I correctly model the next step?
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.