The following table represents undergraduate students at a local university. One student is chosen at random.   Freshman Sophomore Junior Senior Total Live On Campus 3067 4995 3893 3513 15468 Live Off Campus 3561 4589 4469 1777 14396 Total 6628 9584 8362 5290 29864   Find the probability that the student lives off campus or is a junior.  Find the probability that the student lives on campus and is a senior.  Find the probability that the student is a freshman given that they live on campus.  Are the events Freshman and Live on Campus mutually exclusive (or disjoint)? Yes No Why? conditional probability P(Freshman | Live On Campus) is P(Freshman) P(Freshman and Live On Campus) is NOT 0 P(Freshman and Live On Campus) is 0 there are freshman that lives on campus P(Freshman and Live On Campus) is NOT P(Freshman)*P(Live On Campus) P(Freshman and Live On Campus) is NOT P(Freshman)*P(Live On Campus) Are the events Freshman and Live on Campus independent according to probability? Yes No Why? conditional probability P(Freshman | Live On Campus) is P(Freshman) P(Freshman and Live On Campus) is NOT 0 P(Freshman and Live On Campus) is 0 there are freshman that lives on campus P(Freshman and Live On Campus) is NOT P(Freshman)*P(Live On Campus) P(Freshman and Live On Campus) is P(Freshman)*P(Live On Campus)

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