The probability that an automobile being filled with gasoline also needs an oil change is 0.35; the probability that it needs a new oil filter is 0.25; and the probability that both the oil and the filter need changing is 0.24. 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 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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8. The probability that an automobile being filled with gasoline also needs an oil change is 0.35;
the probability that it needs a new oil filter is 0.25; and the probability that both the oil and the
filter need changing is 0.24.
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?
Transcribed Image Text:8. The probability that an automobile being filled with gasoline also needs an oil change is 0.35; the probability that it needs a new oil filter is 0.25; and the probability that both the oil and the filter need changing is 0.24. 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?
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