The probability that an automobile being filled with gasoline will also need an oil change is 0.25; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.14.
(a) If the oil had 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?