CS174 Midterm Sept. 25, 2003 1. Let A and B be events in the same sample space, such that Pr(A) = 2/5, Pr(B) = 3/10 and Pr(A|B) = 2/3. What is Pr(B|A)? 2. In a permutation = (1), (2), ., (n), index i is called a cumulative maximum if (i)=max(1),(2),.,(i).
<!-cs174, final examination, fall/1998->
CS 174 Fall 98 Final Examination
Read these instructions carefully 1. This is a closed book exam. Calculators are permitted. 2. This midterm consists of 14 questions. The first ten questions are multiple cho
Name CS-174 David Wolfe Final
1 May 19, 1992
There are 6 problems marked (E) , and 4 problems (H) . Each question is 10 points, but your two highest scores on a (H) question are doubled. (It is possible to score 120 points.) 90 points is enough for
Name CS-174 David Wolfe Quiz 2
1 February 27, 1992
1. Start with a cycle on n edges and n nodes. Then remove each edge with probability 1 ; p. Give an expression for the expected number of paths remaining in the graph. (Hint: How many paths of leng
Name CS-174 David Wolfe Exam
1 April 28, 1992
There are 4 easier problems marked (E) , and 3 harder problems (H) . Each question is 10 points, but your highest score on a hard question is tripled. 60 points is enough for an A on the exam, so a stud
CS 174, Midterm Exam #2, Spring 1996
CS 174 Spring 1996 Midterm Exam 2 Professor M. Blum
Problem #1 MUFFLER MANIA (OR, TURNING 2-SIDED COINS INTO 3-SIDED COINS) Allison, Barbara, and Cindy are walking in the field one day when they find a muffler.
CS 174: Combinatorics and Discrete Probability
Fall 2012
Homework 1 Solutions
Problem 1. (Exercise 1.1 from MU) We ip a fair coin ten times. Find the probability of the
following events. [Total: 5 points]
(a) The number of heads and the number of tails ar
CS174
CS174
Fall, 2002
Fall
Midterm 1
Except for Problem 8 you are only required to write down the answers. If you wish to show your work, do
so in the space provided. If you need more space, use the back of the page and indicate on the front that you
are
CS174, Fall, 2004, Midterm 1, Professor Richard M. Karp 1. Consider two boxes, the first containing one black and one white marble, and the second containing two black and one white marble. A box is selected at random and a marble is drawn from it at rand
CS 174, Fall, 05, Steiger Instructions: Do all your work in the blue exam books. Please write your answers IN THE GIVEN ORDER, though you may solve problems in any order. There is no need to reduce answers to simplest terms. You may use one page of prepar
CS174
October 11,2001
TEST 1 Instructions: Do all your work in the blue exam books. Please write your answers IN
THE GIVEN ORDER, though you may solve problems in any order. There is no need to reduce answers to simplest terms. You may use one page
CS 174, Midterm #1, Fall 1998>
CS 174, Fall 1998 Midterm 1 Professor A. Sinclair
Read these instructions carefully 1. This is a closed book exam. Caculators are permitted 2. This midterm consists of 10 questions. The first seven questions are multip
CS174 J. Canny
Midterm 2
Spring 98 April 7
This is a closed-book exam with 4 questions. The marks for each question are shown in parentheses, and the total is 60 points. Make sure you allocate enough time to attempt all the questions. You are allo
CS174 J. Canny
Final Exam
Spring 98 May 20
This is a closed-book exam with 6 questions. The marks for each question are shown in parentheses, and the total is 120 points. Make sure you allocate enough time to attempt all the questions. You are all
CS174 J. Canny
Midterm 2
Spring 99 April 6
This is a closed-book exam with 4 questions. You are allowed to use the 4 sides of notes that you brought with you. The marks for each question are shown in parentheses, and the total is 80 points. Make s
CS174 J. Canny
Final Exam
Spring 99 May 19
This is a closed-book exam with 6 questions. You have 3 hours. All questions are worth equal points, so be sure to budget 30 minutes per question. You are allowed to use the 4 sides of notes you brought w
CS174 J. Canny
Midterm 1
Spring 99 Mar 2
This is a closed-book exam with 4 questions. You have 80 minutes. All questions are worth equal points, so be sure to budget 20 minutes per question. You are allowed to use the formula sheet that will be ha
CS174 J. Canny
Final Exam Solutions
Spring 2000 May 17
1. (20 points) (a) (4 points) What is the probability that a random permutation of 1; : : : ; n has at least one fixed point? Assume n is large. The number of fixed points in a random permutat
CS174 J. Canny
Final Exam Solutions
Spring 2001 May 16
1. Give a short answer for each of the following questions: (a) (4 points) Suppose two fair coins are tossed. Let X be 1 if the first coin is heads, 0 if the first coin is a tail. Let Y be 1 i
CS174
CS174 Spring 98 Feb24 J. Canny MIDTERM I This is a closed book exam with 5 questions. You are allowed to use the formula sheet that will be handed out with the exam. No other notes are allowed. Calculators are OK. Write all your answers in thi