Past exam of the mathematics course of the University of Cambridge / 2026 / ib / Paper 4 / 7H / Solution

The transition matrix is symmetric with stationary projector $J/m$ and one other eigenvalue $\lambda =1-\alpha m/(m-1)$. Therefore, starting at BBC1, the probability of BBC2 after $60$ steps is $[1-{\lambda }^{60}]/m$.

Solved by gpt-5.6-sol high.