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Question 5 [Total 10 marks] (Correct your final answers to 4 decimal places) (a) The following table shows the age distributions by gender of confirmed cases of a certain novel virus (each group has 100 cases). U=5 Age Group Below 20 20 to below 40 40 to below 60 60 to below 80 80 or above Group 1 15 12 28 30 15 Group 2 12 9 24 38 - U 17 + U If a case is chosen at random, find the probability that this case is from Group 2 or the case was aged at "20 to below 40" or "80 or above"? (3 marks) (b) Suppose the age distribution of all confirmed cases of this novel virus in Hong Kong is exactly the same as the distribution in part (a) above. If cases are randomly investigated one by one, what is the probability that the first case aged at "80 or above" is identified at the 4th investigation? (3 marks) (c) The number of people visiting a certain clinic follows a Poisson distribution with a mean rate of 5 persons per hour. If the clinic operates 8 hours on a working day, find the probability that there are exactly 41 or 42 people visited this clinic in a randomly selected working day. (4 marks)