At a certain gas station, 40% of the customers use regulargas(A1), 35 % use plus gas (A2) and 25 % usepremium (A3). Of those customers using regular gas, only30 % fill their tanks(event B). Of those customers using plus, 60 %fill their their tanks, whereas of those premium, 50 % fill theretanks.

a) What is the probability that the next customer will requestplus gas and fill their tank ?

b) What is the probability that the next customer fills thetank ?

c)If the next customer fills the tank, what is the probabilitythat the regular gas is requested?

  a) 21%

  b) 45.5%

  c) 26.4%

Step-by-step explanation:

Given the supplied information, a table of probabilities can be constructed. (See the attachment.) The numbers across the bottom reflect the given ratios of customers selecting the different gas types. The numbers in the cells are those bottom numbers multiplied by the percentage that fill the tank (or not). The numbers on the right are the sums of the numbers in each row.

a) The top center cell in the table answers this question. It it the product ...

  p(plus)×p(fill | plus) = 0.35×0.60 = 0.21 = 21%

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b) The sum on the right answers this question:

  p(fill) = 45.5%

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c) The ratio of the first column number (12%) to the row sum for Fill (45.5%) answers this question:

  p(regular | fill) = 12%/45.5% ≈ 26.4%