This preview shows pages 1–11. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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, 79p, Loomis 141. Email Cinda with conflicts. Todays lecture covers material from Rosen, sections 5.25.3. 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(EF) is defined to be: Pr(EF) = Pr(E F)/Pr(F). F E Cs173  Spring 2004 CS 173 Conditional Probability Pr(EF) = 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(EF) = 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)....
View
Full
Document
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.
 Spring '08
 FLECK@SHAFFER

Click to edit the document details