The probability that an automobile being inspected will need an oil change is 0.
ID: 3276575 • Letter: T
Question
The probability that an automobile being inspected will need an oil change is 0.25; the probability that it needs a new air filter is 0.40; and the probability that both the oil and air filter need changing is 0.14. a. What is the probability that the vehicle needs either the oil change or the air filter? b. What is the probability that the vehicle needs neither the oil change nor the air filter? Given that the vehicle was found to need an oil change, what's the probability that it also needs a new air filter? c.Explanation / Answer
a) P(Either oil change or air filter)
= P(Oil Change) + P(Air Filter) - P(Both)
= 0.25 + 0.40 - 0.14
= 0.51
b) P(Neither oil change nor air filter)
= 1 - P(At least one)
= 1 - 0.51 [From part a)]
= 0.49
c) P(Air filter | Oil change)
= P(Air filer and oil change)/P(Oil change)
= 0.14/0.25
= 14/25
= 0.56
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