Question: Section C Long Questions (45 marks) Answer ALL questions in this section. Each question carries 15 marks. 13. (a) A pack of red pockets contains

Section C Long Questions (45 marks) Answer ALL questions in this section. Each question carries 15 marks. 13. (a) A pack of red pockets contains nine $10 banknotes, sixteen $20 banknotes, three $50 banknotes and two $100 banknotes. (i) How many red pockets are there in the pack? (1 mark) (ii) A red pocket is drawn out randomly. What is the expected value of the money obtained? (3 marks) (b) Billy, John and Peter will run for a ten-mile race. The probabilities of finishing the race within 1 hour are 0.9, 0.7 and 0.6 for Billy, John and Peter respectively. Correct your answers to 3 decimal places. (i) Find the probability that all of them can finish the race within 1 hour. (2 marks) (ii) Find the probability that all of them fail to finish the race within 1 hour. (3 marks) (iii) Find the probability that at least one of them finishes the race within 1 hour. (3 marks) (iv) Find the probability that exactly one of them finishes the race within 1 hour

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