The probability that an automobile being filled with gasoline also needs an oil change is 0.30; the probability that it needs a new oil filter is 0.45; and the probability that both the oil and the filter need changing is 0.14. (a) If the oil has to be changed, what is the probability that a new oil filter is needed? (b) If a new oil filter is needed, what is the probability that the oil has to be changed?

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