11ProbHw1

# 11ProbHw1 - IEOR 3658 Probability Prof Mariana...

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IEOR 3658 Assignment #1 Probability September 13, 2011 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #1 – due September 21st, 2011 1. Consider two subsets A,B Ω and suppose x 1 ,x 2 A , x 2 B , but x 1 / B . For each of the following statements, determine whether it is true, possibly true (not enough information is available to decide), or false: (a) A B (b) B A (c) A = B (d) A 6 = B (e) ∅ ⊂ A (f) A = Ω (g) B B 2. Draw Venn diagrams and ﬁnd a simple expression for the following events: (a) ( E F ) ( E F c ) (b) ( E F ) ( E c F ) ( E F c ) (c) ( E F ) ( F G ) 3. Let E , F and G be three events. Find expressions for the following events: (a) only F occurs (b) both E and F but not G occur (c) at least one event occurs (d) none occurs (e) at most two occur 4. Let A,B,C be three subsets of Ω about which it is known that A = B C and also A = B C . For each of the following, state whether it is true, possibly true, or false:

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## This note was uploaded on 12/11/2011 for the course IEOR 3658 taught by Professor Olvera during the Fall '08 term at Columbia.

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11ProbHw1 - IEOR 3658 Probability Prof Mariana...

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