lec0328 - CS 173: Discrete Mathematical Structures Cinda...

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Unformatted text preview: CS 173: Discrete Mathematical Structures Cinda Heeren heeren@cs.uiuc.edu Siebel Center, rm 2213 Office Hours: BY APPOINTMENT Cs173 - Spring 2004 CS 173 Announcements Homework 9 available. Due 04/02, 8a. Exam 2, Apr 4, 7-9p, Loomis 141. Email Cinda with conflicts. Todays lecture covers material from Rosen, sections 5.2-5.3. Cs173 - Spring 2004 CS 173 Probability Which is more likely: a) Rolling an 8 when 2 dice are rolled? b) Rolling an 8 when 3 dice are rolled? c) No clue. Cs173 - Spring 2004 CS 173 Probability What is the probability of a total of 8 when 2 dice are rolled? What is the size of the sample space? 36 How many rolls satisfy our condition of interest? 5 So the probability is 5/36. Cs173 - Spring 2004 CS 173 Probability What is the probability of a total of 8 when 3 dice are rolled? What is the size of the sample space? 216 How many rolls satisfy our condition of interest? C(7,2) So the probability is 21/216. Cs173 - Spring 2004 CS 173 Conditional Probability Let E and F be events with Pr(F) > 0. The conditional probability of E given F, denoted by Pr(E|F) is defined to be: Pr(E|F) = Pr(E F)/Pr(F). F E Cs173 - Spring 2004 CS 173 Conditional Probability Pr(E|F) = Pr(E F)/Pr(F). A bit string of length 4 is generated at random so that each of the 16 bit strings is equally likely. What is the probability that it contains at least two consecutive 0s, given that its first bit is a 0? Pr(F) = 1/2 Pr(E F)? 0000 0001 0010 0011 0100 Pr(E F) = 5/16 Pr(E|F) = 5/8 Cs173 - Spring 2004 CS 173 Independence The events E and F are independent if and only if Pr(E F) = Pr(E) x Pr(F). Let E be the event that a family of n children has children of both sexes. Lef F be the event that a family of n children has at most one boy. Are E and F independent if n = 2? No Cs173 - Spring 2004 CS 173 Independence The events E and F are independent if and only if Pr(E F) = Pr(E) x Pr(F). Let E be the event that a family of n children has children of both sexes. Lef F be the event that a family of n children has at most one boy. Are E and F independent if n = 3? Yes Cs173 - Spring 2004 CS 173 Independence The events E and F are independent if and only if Pr(E F) = Pr(E) x Pr(F)....
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This note was uploaded on 09/15/2008 for the course CS 173 taught by Professor Fleck@shaffer during the Spring '08 term at University of Illinois at Urbana–Champaign.

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lec0328 - CS 173: Discrete Mathematical Structures Cinda...

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