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L. the probability that a car needs an oil change is .30. the probability that an automobile being filled with gasoline also needs an oil change is 0.20; and the probability that both the oil and the filter need changing is 0.10. what is the probability that a new oil filter is needed given that its' oil is being changed?

Respuesta :

Denote by A the event "A new oil filter is needed"
Denote by B the event " The car  oil is being changed"
We have the formula:
[tex]P(A/B)=\frac{P(A\cap B)}{P(B)}\text{ also }P(B)=1-P(\bar{B})=1-0.3=0.7\\P(A\cap B)=0.10\text{ (Given)}\\\text{Now we can evaluate the probability:}\\P(A/B)=\frac{0.10}{0.7}=0.14[/tex]. "


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