Hello, alderon!

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?