We are looking at cars that fill fuel where it is also possible to change oil an

Question

We are looking at cars that fill fuel where it is also possible to change oil and fill the liquid. The likelihood that a car must change oil is 0.25.

The likelihood that a car must recharge fluid is 0.40 and the likelihood for a car both need oil change and filling fluid is 0.14. Define the events O: Oil change and S: Spray fluid. Here you may want to draw friend charts.

a) A fuel-fired vehicle must fill the spray fluid, what is the probability that oil must also be replaced?
b) What is the likelihood that the car will only need to fill the fluid?

c) Are events S and O independent?

Explanation / Answer

a) probability that oil must also be replaced ; given  vehicle must fill the spray fluid =P(O|S) =P(OnS)/P(S)

=0.14/0.40 =7/20

b)  likelihood that the car will only need to fill the fluid =P(S)-P(SnO) =0.40-0.14=0.26

c) as P(S)*P(O) =0.25*0.40=0.40 which is not equal to P(SnO)=0.14 . therefore S and O are not independent.

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