Use Bayes' Theorem: .
We are given: .The probability that a car will need an oil change is 25%.
The probability that it needs a new filter is 40%.
The probabilty that both the oil and filter need changing is 14%.
a) If the oil had to be changed, what is the probabilty that a new filter is needed?
b) If the filter had to be changed, what is the probability that the oil is changed?