A-Level Further Maths · Further Statistics
Markov Chains
What is it
A Markov chain models a system that moves between a fixed set of states, where the probability of moving to the next state depends only on the current state, not on the sequence of states that came before it.
Why it matters
Markov chains model an enormous range of real systems — weather patterns, website navigation, board game positions, genetic sequences — anywhere the future depends only on the present state, not the full history.
Exam tip
Draw the transition diagram before setting up the transition matrix — visualising the states and probabilities first makes it far easier to check that the probabilities from each state genuinely sum to 1.
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