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m1-09

# m1-09 - STOR 435 Exam 1 Fall 2009(1 Assume that events A...

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STOR 435 Exam 1 Fall 2009 (1) Assume that events A and B are independent, events A and C are independent, and B C . Moreover, P ( A ) = 1 / 3, P ( B ) = 1 / 4, and P ( C ) = 1 / 2. (a) Draw a Venn diagram. (b) Calculate P ( A B c C ). (c) Calculate P ( C | A c B c ). (d) Calculate P ( B or C | A ). (2) 8 people (5 women and 3 men) are divided into two diﬀerent groups of equal size. (a) What is the probability that Group 1 consists of an equal number of men and women? (b) Given that Group 1 contains at least 1 woman, what is the conditional probability that Group 2 contains more women than men? (3) The curriculum in a certain high school is designed according to 3 diﬀerent career paths, denoted by C 1 , C 2 and C 3 . The proportions of students in these 3 paths are 50%, 30% and 20% respectively. Suppose 20% of the students in C 1 , 15% of the students in C 2 and 10% of the students in C 3 have their GPA “3.5 or higher”. (a) Construct a tree diagram.

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m1-09 - STOR 435 Exam 1 Fall 2009(1 Assume that events A...

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