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# HW1 - IE 111 Fall Semester 2007 Homework#1 Due Wednesday...

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IE 111 Fall Semester 2007 Homework #1 Due Wednesday 9/5/07 Question 1. Consider the Venn diagram at right with events A, B, C, and D as shown when you answer questions a) through e). a) Give a set representation of the shaded region. Indicate the most appropriate answer for each of the following questions (where NMI means “need more information”). b) T F NMI (A B ) D and (A D) C are mutually exclusive. c) T F NMI B and C are independent d) T F NMI P(A|B) ≥ P(B|A) e) T F NMI P(B) ≤ P(D) Question 2. A Lehigh student is selected at random and the student’s class x (Frosh, Soph, junior, Senior, or Grad), sex y (Male, Female), and living arrangement z (dorm, frat, sorority, off-campus) are observed. Note the following Lehigh rules: - Frosh must live in dorms. - Frats are limited to under grad men, sororities to under grad women. - Grad students must live off campus. a) Describe the sample space of this experiment by listing its elements in the form (x,y,z). b) Use a tree diagram to describe the sample space in question 1. Question 3. An experiment consists of throwing a pair of dice, one maize (yellow), and the other blue. If x is the number showing on the maize die, and y is the number showing on the blue die, then an outcome can be represented as (x,y).

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