At a certain gas station, 70% of customers use unleaded gas, 20% of customers us

Question

At a certain gas station, 70% of customers use unleaded gas, 20% of customers use premium gas, and the rest use diesel. Of those customers using unleaded gas 60% fill their tank to the full. Of those customers using premium, 90% fill their tank to the full, whereas those using diesel 30% fill their car's tank to the full. Users of gas types and filling of tanks is shown in the following tree diagram: Tree= [Answer all questions below to 3 decomal places. The answers must be given as a fraction, not percentage. For instance, if the answer is 20.7% , it must be typed as 0.207.] a)What is the probability that a randomly chosen customer uses diesel and filled her car's tank to the full? i.e. P(Diesel ? Full) = b)What is the probability that a randomly chosen customer filled her car's tank to the full? i.e. P(Full) = c)If a randomly selected customer filled her car's tank to the full, what is the probability that she uses diesel? i.e. P(Diesel | Full) =

Explanation / Answer

a) probability that a randomly chosen customer uses diesel and filled her car's tank to the full

=(1-0.7-0.2)*0.30 =0.03

b)

P(Full)=P(unleaded and full)+P(premium and full)+P(diesel and full)=0.7*0.60+0.2*0.9+0.1*0.30=0.63

c)

P(Diesel | Full) =P(Diesel ? Full)/P(full)=0.03/0.63=0.0476

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