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 0.12. (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? (a) The probability that a new oil filter is needed is (Round to three decimal places as needed.) (b) The probability that the oil needs to be changed is (Round to three decimal places as needed.)

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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 0.12.
(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?
(a) The probability that a new oil filter is needed is
(Round to three decimal places as needed.)
(b) The probability that the oil needs to be changed is.
(Round to three decimal places as needed.)
Transcribed Image Text: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 0.12. (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? (a) The probability that a new oil filter is needed is (Round to three decimal places as needed.) (b) The probability that the oil needs to be changed is. (Round to three decimal places as needed.)
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