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Ex General Probability

Ex General Probability - Stat 225 Examples 1 At the end of...

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Stat 225 Examples (9-3-08) 1. At the end of the semester, a statistics professor examines the grades for his 40 students. He notices that 5 students received A’s on the two midterms and the final, while 20 students did not receive an A on any of the three exams. There were 9 students who received A’s on both midterms. There were 8 students who received A’s on the 1 st midterm and the final, but only 6 students who received A’s on the 2 nd midterm and the final. In total 15 students received an A on the 1 st midterm and 12 received an A on the 2 nd midterm. Using the inclusion-exclusion principle, how many students received an A on the final but did not get A’s on either midterm? Now, draw a Venn diagram with the numbers filled in. (Hint, you should be able to write in words what each particular section means.) 2. Suppose a given university has only 3 departments: Math, English, and History. Enrollment information reveals that 23% of students take Math courses, 50% take English courses, and 36% take History courses. Only 3% of students take courses
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