IB Maths AI HL AI 4.5 Markov chains questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Question 1

Paper 1Easy6 marks

A campus club records which of two cafés its members visit each Friday. The transition diagram in Figure 1 gives the probabilities that a member visits each café on the next Friday, based on the café visited this Friday.

Let $s_n$ be the column state matrix after $n$ weekly transitions, using the state order North, South. On the Friday of the survey, the state matrix is

s_0=\begin{pmatrix}0.75\\0.25\end{pmatrix}.

(a)

Write down the transition matrix $T$ where $T_{ij}$ is the probability of moving from state $j$ to state $i$

[2]

(b)

Calculate $s_1=Ts_0$

[2]

(c)

Hence, using your result from part (b), calculate $s_2$

[2]

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