MATH 1150 Lecture Notes - Lecture 15: Empirical Probability

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C= owns a cat: p(c|d) = p(. 17)/p(. 44) = . 386, p(d|c) = p(. 17)/p(. 29) = . 654, p(c or d) = p(c) + p(d) p(c and d) = p(. 29) + p(. 44) p(. 17) = . 56. Sum = 7 is the event the dice sum to 7 and d = 4 event that the first die lands on a four. Is getting a sum of 7 independent of the first die landing on four: p(s=7) x p(d=4) (6/36) x (1/6) = 1/36, p(s and d) = 1/36, 55% of students at the university are female (f). 30% of students at the university graduate in four years (g). 13% of all students at the university are women who graduate in four years: are gender and graduating in four years independent, p(f) x p(g) = p(f and g) (. 55) x (. 30) = (. 13) . 165 and . 13 are not equal, therefore they are not independent: example, the probability that people prefer to shop online = . 70.

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