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2. A regional telephone company operates three identical relay stations at different locations. During a one-year period, the number of malfunctions reported by each stations and the causes are shown below. Suppose that a malfunction was reported and it was found to be caused by other human errors. (a) What is the probability that the malfunction is caused by human error? (Give answer in simplified fraction form. Ex. 31/51) (b) What is the probability that the human error was caused by station C? (Give answer in simplified fraction form. Ex. 31/51) (c) What is the probability that the human error was caused by station B? (Give answer in simplified fraction form. Ex. 31/51) (d) After a year, it was observed that the 1 in 4 malfunctions by human error was caused by station B. Basing on last year's data and still considering human errors, what is the new probability that the station B caused the malfunction.
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