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25. (30 marks) Eric can come to the University on 4 modes of transport: by bus, by MTR, on foot or on bicycle. If he takes the bus, his chances of coming to class late are 0.13. If he takes the MTR, he will never be late. On the other hand, if he goes on foot or on a bicycle, his chances of being late are 0.95 and 0.29, respectively. Suppose, on average, Eric comes to class by bus 30% of the time, by MTR 30% of the time, on foot 10% of the time and on his bicycle the rest of the time. (a) Calculate the overall probability that Eric can arrive to class on time. (b) Suppose Eric came to class on time today. Calculate the probability that he has taken the MTR. (c) Using part (b), show that the following comment suffers from the confusion of inverse: \"Since Eric is never late when he takes the MTR, therefore if he is on time that means he must have taken the MTR\". (d) Show that the following comment also suffers from the confusion of inverse: \"Since Eric is late 95% of the times when he goes on foot (0.95), therefore if he is late that means he must have come to university on foot\