After easing the Covid- 19 restrictions in Melbourne, transport choices have changed for many people. We are interested in exploring patterns around which modes students have used since the start of 2022, considering which of these they used at least once. The following data is calculated for 165 students: 57 used public transport (e.g., train, bus, tram) 41 used hired micromobility services (e.g., hired scooters or e-bikes) 63 used private wheeled transport (e.g., own car or bike) 12 used public transport and micro mobility 18 used private and public transport 7 used public transport, private transport and micromobility services 42 did not use any of the above transport modes (e.g., walked only)

a. [1 mark] *A value needed for the Venn diagram is missing. Explain how to formally find it and calculate the missing value. b. [3 marks] * Draw a Venn diagram with each mode group as a set and label each part of the diagram with the correct values. c. [3 marks] * Provide counts for the following. **Show the numerical expression** using the values from the Venn diagram you used to find your answer: correct answers without expressions will be awarded 0 marks. i. Did not use micromobility services. ii. Used public transport, but did not use private transport iii. Did one only of private, public, and micromobility transport. d. [1.5 marks] ** Using each mode group as a set, represent the following using set operators (U: union, : intersection, C or ': complement): i. Used both public and private transport. ii. Did not use private transport nor public transport. iii. Used micromobility services and private transport but did not use public transport.