Answer:
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%
