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Date November 2021 Marks available 2 Reference code 21N.1.AHL.TZ0.9
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Complete Question number 9 Adapted from N/A

Question

Katie likes to cycle to work as much as possible. If Katie 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.

Complete the following transition diagram to represent this information.

[2]
a.

Katie works for 180 days in a year.

Find the probability that Katie cycles to work on her final working day of the year.

[3]
b.

Markscheme

           A1A1


[2 marks]

a.

A=0.80.60.20.4               (A1)

A180=0.750.750.250.25               (M1)

0.75               A1


[3 marks]

b.

Examiners report

This question was often done well. Many textbooks teach the method of multiplying the transition matrix by an initial state vector. This was often seen in candidates’ responses. eg 0.80.60.20.418010=0.750.25. Errors were often due to the figures being incorrectly placed in the transition matrix; not just the transpose, but other combinations of the four values as well.

a.

This question was often done well. Many textbooks teach the method of multiplying the transition matrix by an initial state vector. This was often seen in candidates’ responses. eg 0.80.60.20.418010=0.750.25. Errors were often due to the figures being incorrectly placed in the transition matrix; not just the transpose, but other combinations of the four values as well.

b.

Syllabus sections

Topic 4—Statistics and probability » AHL 4.19—Transition matrices – Markov chains
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Topic 4—Statistics and probability

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