At a certain gas station, 55% of customers use unleaded gas, 35% or customers us

Question

At a certain gas station, 55% of customers use unleaded gas, 35% or customers use premium gas, and the rest use diesel. Of those customers using unleaded gas 80% fill their tank to the full. Of those customers using premium 20% fill their tank to the full, whereas those using diesel 60% fill their car's tank to the full. Users of gas types and filling of tanks is shown in the following tree diagram: Unleaded Premium Diesel Full Full Full( Full Full [Answer all questions below to 3 decom al 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.] What is the probability that a randomly chosen customer uses diesel and filled her car's tank to the full? i.e. PDieseln Full)- Submit Answor Tries o/s What is the probability that a randomly chosen customer filled her car's tank to the full? l.e. P(Full) Submit Answer Tries 0/5 If a randomly selected customer filled her car's tank to the full, what is the probability that she uses diesel? i.e. P(DieselFull) Submit Answer Tries o/s e. PFull) My.generapreferences on what is marked 3s NEW

Explanation / Answer

P(unleaded)=0.55
P(premium)=0.35
P(Diesel)=0.10
P(Full | unleaded)=0.80
P(Full premium )=0.20
P(Full | Diesel)=0.60

a)
the probabilty that a randomly chosen customer uses diesel and filled her car's tank to the full
P(Full | diesel)*P(Diesel)=0.60*0.1=0.06

b)
P(Full)=0.55*0.8+0.35*0.2+0.1*0.6=0.57

c)
P(Diesel | Full )=P(Diesel and Full)/P(Full)
=0.06/0.57
=0.10526

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