Answer to Question #159022 in Statistics and Probability for asim

Question

The probability that an automobile being filled with gasoline will also need an oil change is 0.35; the probability that it needs a new oil filter is 0.45; and the probability that both the oil and filter need changing is 0.25.

(i) If the oil had to be changed, what is the probability that a new oil filter is needed ?

(ii) If a new oil filter is needed, what is the probability that the oil has to be changed ?

Answer 1

We denote by A the event that an automobile being filled with gasoline will also need an oil change and by B the event that an automobile being filled with gasoline needs a new oil filter.

Then P(A) = 0.35, P(B) = 0.45 and P(AB) = 0.25.

(i) The conditional probability that a new oil filter is needed, If the oil had to be changed, is equal to P(B|A) = P(AB)/P(A) = 0.25/0.35 = 5/7 = 0.7143

(ii) The conditional probability that the oil has to be changed If a new oil filter is needed, is equal to P(A|B) = P(AB)/P(B) = 0.25/0.45 = 5/9 = 0.5556

Answer. (i) 71.43%, (ii) 55.56%