Requirements for high school graduation. In Italy, all high school students must take a high school diploma (HSD) exam and write a paper in order to graduate. In Organizational Behavior and Human Decision Processes (July 2000), University of Milan researcher L. Macchi provided the following information to a group of college undergraduates. Fact I:In Italy, 360 out of every 1,000 students fail their HSD exam. Fact2: Of those who fail the HSD, 75% also fail the written paper. Fact 3:Of those who pass the HSD, only 20% fail the written paper. Define events A and Bas follows:
A = {The student fails the HSD exam.}
B ={The student fails the written paper.}
a. Write Fact 1 as a probability statement involving events A and/or B.
b. Write Fact 2 as a probability statement involving events A and/or B.
c. Write Fact 3 as a probability statement involving events A and/or B.
d. State P(A ⋂ B) in the words of the problem.
e. Find P(A ⋂ B).
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