65% of students in a statistics class said that they liked statistics more than algebra. if 3 of these students are randomly selected, what is the probability that all 3 students said that they liked statistics more than algebra? express your answer as a decimal rounded to the thousandths place.

The answer to this question depends on the class size. However if we assume the class is sufficiently large then we can assume the 65% ratio stays relatively constant as students are selected. In this case we will treat selecting three students as independent events. Therefore we can multiply the probabilities. Finally, the probability of selecting three students that all like statistics more than algebra is (0.65)x(0.65)x(0.65) = 0.275.

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