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4. The probability that a bus is full is 0.2. If the bus is full, the probability that Caroline is late to work is 0.8. If the bus is not full, the probability that Caroline is late to work is 0.15. (a) Draw a tree diagram to represent this information. (3) (b) Find the probability that Caroline is late to work. (2) (c) Find the probability that the bus is full given that Caroline is late to work. (2) 5. A group of 120 people were asked if they preferred tea, coffee or hot chocolate. Of these people, 66 prefer cake and the rest prefer biscuits with their hot drink. 40 people prefer tea of whom 26 prefer cake. 43 people prefer hot chocolate of whom 30 prefer cake a) Complete a two-way table to show this information. (3) A person is chosen at random. Find the probability that this person: b) prefers coffee (1) c) prefers biscuits given that theirr prefer coffee (2) 6) Two events A and B are independent, such that PM) = 0.4 and PM ('1 B) = 0.12. a) Find P(B) b) Find PM U B) A third event C has P(C) = 0.3. A and C are mutually exclusive and P(B n C) = 0.1 c) Draw a Venn diagram to represent the complete sample space for the events A, B and C. d) Find P(B IC) e) Find P(B n (AU (2)) (1) (1) (3) (2) (1)