At a garage, they classify cars in three categories, new, elderly and old cars. They have experienced that 65% of all checked cars are new {P(N)=0.65} and 25% are elderly {P(E)=0.25}. They have also experienced that the probability for detecting a major flaw on a new car 0,15{P(F|N)=0,15}, on an elderly car 0,25{P(F|E)=0,25} and on an old car 0,85{P(F|O)=0,85}.
What is the probability that they do not find a major flaw on a new car, {P(F|N)}?
What is the probability, that a car, that arrives for a check is a new car without major flaws, {P(N∩F)}?
What is the probability that a car that arrives for a check has major flaws, {P(F)}?
What is the probability, that a car with major flaws is new, {P(N|F)}?
Is the event, a car with major flaws, independent of the car's age? You need to substantiate your arguments with theory.