Lesson_03_sol_prob - Probability - Solutions 1 Situation:...

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Probability - Solutions 1 Situation: The High School and Beyond data is from a large-scale longitudinal study conducted by the National Opinion Research Center (1980) under contract with the National Center for Education Statistics. Below is a table representing a sample of 100 students from this data that includes the student’s gender and whether the high school they attended was public or private. Let A denote the subset of these 100 subjects that the student is Female, so the event A = {Female}. Similarly define event B as the student attended a Public high school, so the event B = {Public}. . The following 2x2 table classifies each student according to gender and school type. Public Private Total Female 38 7 45 Male 46 9 55 Total 84 16 100 For example, the table reveals that 38 students were both Female and attended a Public high school, so: P(A ∩ B) = 38/100 = 0.38 (read “the probability of A and B is 0.38)). a. Fill in the marginal totals of the table (the row and column totals). From these totals determine the probability that the student is Female and also the probability the student attended a Public high school. Answer the following placing the proper event notation (e.g. A, B) in the ( ). P(Female) = P( A ) = .45 P(Public) = P( B ) = .84 b. Translate the following events into set notation using the symbols A and B, complement, union, intersection. Also give the probability of the event as determined from the table above. Fill in the table below with these values. {If you cannot construct the symbol ∩, just use & or copy and paste} Lastly, draw a Venn diagram (on scratch paper, but you need not submit it) showing the events of Female, Public, and both Female and Public. The first one is completed for you. Event in words
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