# lec0316 - CS 173 Discrete Mathematical Structures Cinda...

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CS 173: Discrete Mathematical Structures Cinda Heeren [email protected] Siebel Center, rm 2213 Office Hours: BY APPOINTMENT

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Cs173 - Spring 2004 CS 173 Announcements Homework 8 available. Due 03/ 26, 8a. Exam 2, Apr 4, 7-9p, Loomis 141. Email Cinda with conflicts. Today’s lecture covers material from Rosen, sections 5.1-5.3.
Cs173 - Spring 2004 CS 173 A little practice In an RNA chain of 20 bases, there are 4 As, 5 Us, 6 Gs, and 5Cs. If the chain begins either AC or UG, how many such chains are there? Let A denote the set of chains beginning with AC, and U denote the set of chains beginning with UG. Count them separately, and then sum. First find | A| : 18 bases, 3 As, 5 Us, 6 Gs, and 4Cs. (This is like the MISSISSIPPI problem.) | A| = 18!/ (3!5!6!4!)

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Cs173 - Spring 2004 CS 173 Probability We roll a single die, what are the possible outcomes? {1,2,3,4,5,6} The set of possible outcomes is called the sample space. Depends on what we’re going to ask. Often convenient to choose a sample space of equally likely events. {(1,1),(1,2),(1,3),…,(6,6)} We roll a pair of dice, what is the sample space?
Cs173 - Spring 2004 CS 173 Probability Define a probability measure on a set S to be a real- valued function, Pr, with domain 2 S so that: For any subset A in 2 S , 0 Pr(A) 1. Pr( ) = 0, Pr(S) = 1. If subsets A and B are disjoint, then Pr(A U B) = Pr(A) + Pr(B). Pr(A) is “the probability of event A.” A sample space, together with a probability measure, is called a probability space. S = {1,2,3,4,5,6} For A S, Pr(A) = | A| / | S| Ex. “Prob of an odd #” A = {1,3,5}, Pr(A) = 3/ 6

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Cs173 - Spring 2004 CS 173 Probability Some things you already know: If A is a subset of S, let ~A be the complement of A wrt S. Then Pr(~A) = 1 - Pr(A) If A and B are subsets of S, then Pr(A U B) = Pr(A) + Pr(B) - Pr(A B) A thought to ponder… What if I asked you to pick a random positive integer? Inclusion-Exclusion
CS 173 Probability Choose a door to win a prize! Monty Hall puzzle.

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## This note was uploaded on 09/15/2008 for the course CS 173 taught by Professor [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */ during the Spring '08 term at University of Illinois at Urbana–Champaign.

• Spring '08
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lec0316 - CS 173 Discrete Mathematical Structures Cinda...

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