Question

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?

Answer 1

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:

`P(A/B)=(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)=(0.10)/(0.7)=0.14`. "