Question 1172488
Previously Posted
RE 
type                REG      EXTRA      PREMIUM
 %                  .45        .30        .25
%fill/not fill    .35 .65    .60 .40   .45  .55
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Hi  
ii)What is the probability that the next customer will request premium unleaded gas and will not fill the tank? 
P(Independent Events) = the product of the individual probabilities.
P = {{{highlight_green( .25(.55))}}}
iii)What is the probability that the next customer fill the tank?
mutually exclusive: 
P(A or B or C ) = P(A) + P(B) + p(C)
P = {{{highlight_green(.45(.35) + .30(.60) + .25(40))}}}
iv)Given  that  the  next  customer  fills  the tank.  
What  is  the  probability  that it is extra gas 
P(A|B) = P(A and B)/P(B) Bayes Theorem
P(extra|fills tank) = {{{highlight_green( .30(.60)/(.45(.35) + .30(.60) + .25(40)))}}}
Wish You the Best in your Studies.