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Emily likes to cycle to work as much as possible. If Emily cycles to work one day then she has a probability of 0.2 of not cycling to work on the next work day. If she does not cycle to work one day then she has a probability of 0.4 of not cycling to work on the next work day.

Question

HLPaper 1

Complete the following transition diagram to represent this information.

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Solution

$\boldsymbol{A}=\left(\begin{array}{ll}0.8 & 0.6 \\ 0.2 & 0.4\end{array}\right)$ (A1)

Emily works for 180 days in a year. Find the probability that Emily cycles to work on her final working day of the year.

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Solution

$\boldsymbol{A}^{180}=\left(\begin{array}{ll}0.75 & 0.75 \\ 0.25 & 0.25\end{array}\right)$ (M1)

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Emily likes to cycle to work as much as possible. If Emily cycles to work one day then she has a probability of 0.2 of not cycling to work on the next work day. If she does not cycle to work one day then she has a probability of 0.4 of not cycling to work on the next work day.

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