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A manager of a large office responsible for sustainability conducted a survey amongst her staff to...

A manager of a large office responsible for sustainability conducted a survey amongst her staff to find out how they travelled to work, and how punctual they were. The survey results were, for those surveyed: 25% of the staff took a bus to work, 40% took a car to work and the remainder cycled or walked (the sustainable option). If a staff member took a bus they were late 20% of the time, if a staff member took a car they were late 15% of the time and the remainder (those who cycled or walked) were never late.

(a) Complete the tree diagram below by writing the relevant probabilities on each branch and at the ends of the branches.

(b) Use the tree diagram to answer the following. Write down the calculations needed to find the answers:

(i) What is the probability that a randomly chosen staff member was late to work?

(ii) Given that a staff member was late, what is the probability they came to work by bus?

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