MATH 1300: Finite Mathematics EXAM 3 21 April 2015

Transcription

1 MATH 300: Finite Mathematics EXAM 3 2 April 205 NAME:... SECTION:... INSTRUCTOR:... SCORE Correct (a): /5 = % INSTRUCTIONS. DO NOT OPEN THIS EXAM UNTIL INSTRUCTED TO BY YOUR ROOM LEADER. All exam pages must remain stapled. Do not separate or remove any pages. If you separate or remove any pages from this exam, your score will be reduced. You will have 60 minutes to complete this exam. When the room leader announces pencils down, you must stop writing. Students who continue writing after the pencils down announcement will receive a score of This exam has 9 pages, including the cover sheet. There are 5 multiple choice questions. The answers on your scantron are your FINAL answers. If you change an answer, erase your old answer thoroughly. Only final answers on your scantron will be graded.

2 MATH 300 Spring 205 Exam 3: Name... (a) 2 MULTIPLE CHOICE: Mark your FINAL answers on your scantron.. Two seven-member teams play a game. After the game, each of the members of the winning team shakes hands once with each member of both teams. How many handshakes take place? ➀ 4 ➁ 42 ➂ 49 ➍ An electronics store receives a shipment of 20 graphing calculators, including 6 that are defective. Four of the calculators are selected to be sent to a local high school. How many of the possible selections will contain no defective calculators? ➊ 00 ➁ 4845 ➂ 29,070 ➃ 38,760

3 MATH 300 Spring 205 Exam 3: Name... (a) 3 3. The student council at a certain college is made up of five freshmen, six sophomores, seven juniors, and eight seniors. A yearbook photographer would like to line up two council members from each class for a picture. How many different pictures are possible if each group of classmates stands together? ➀ 2,6,800 ➋ 33,868,800 ➂,4,200 ➃ 88, An experiment consists of tossing a coin ten times and observing the sequence of heads and tails. How many different outcomes have exactly five heads? ➀ 024 ➁ 52 ➂ 256 ➍ 252

4 MATH 300 Spring 205 Exam 3: Name... (a) 4 5. Refer to the map in the figure below. How many of the routes from A to B pass through point C? ➀ 28 ➁ 4 ➌ 20 ➃ How many different committees can be formed from 8 teachers and 39 students if the committee consists of 3 teachers and 2 students? ➀ 32 ➁ 797 ➌ 4,496 ➃ 497,952

5 MATH 300 Spring 205 Exam 3: Name... (a) 5 7. Suppose that a red die and a green die are tossed and the numbers on the sides that face upward are observed. What is the probability that the numbers add up to either 7 or? ➀ ➁ ➂ ➃ ➎ Suppose that Pr(E) = 0.5, Pr(F ) = 0.4, and Pr(E F ) = 0.3. Find Pr(E F ). (You may find it helpful to draw a Venn diagram. Answers are rounded to four decimal places.) ➀ ➁ ➂ ➍

6 MATH 300 Spring 205 Exam 3: Name... (a) 6 9. An urn contains 6 green balls and 9 white balls. A sample of 4 balls is selected at random from the urn. Find the probability that the sample contains more green balls than white balls. (Answers are rounded to four decimal places.) ➀ ➁ ➂ ➍ A factory produces fuses, which are packaged in boxes of 4. Three fuses are selected at random from each box for inspection. The box is rejected if at least one of these three fuses is defective. What is the probability that a box containing five defective fuses will be rejected? (Answers are rounded to four decimal places.) ➊ ➁ ➂ ➃

7 MATH 300 Spring 205 Exam 3: Name... (a) 7. A die is rolled 42 times. What is the probability of getting exactly 9 4 s? (Answers are rounded to four decimal places.) ➀ ➁ ➂ ➍ An airport limousine has four passengers and stops at eleven different hotels. What is the probability that two or more people will be staying at the same hotel? (Assume that each person is just as likely to stay in one hotel as another. Answers are rounded to four decimal places.) ➀ ➋ ➂ ➃ 0.006

8 MATH 300 Spring 205 Exam 3: Name... (a) 8 3. The winner of the Superball Lottery must correctly pick a set of 5 numbers from through 57 and then correctly pick one number (called the superball) from to 4. What are the odds of winning the Superbowl lottery? ➀ to 7,67,346 ➁ to 7,67,347 ➂ 7,67,346 to ➃ to 504,452,79 ➎ 4. Two ordinary quarters and a fake quarter with two heads are placed in a hat. One quarter is selected at random and tossed twice. If the outcome is HH, what is the probability that the fake quarter was selected? ➀ ➁ ➌ ➃

9 MATH 300 Spring 205 Exam 3: Name... (a) 9 5. Colorblindness is a sex-linked, inherited condition that is much more common among men than women. Suppose that 4% of all men and 0.4% of all woman are color-blind. A person is chosen at random and found to be color-blind. What is the probability in percent terms that the person is male? (You may assume that 50% of the population are men and 50% are women. Answers are expressed in percent form rounded to one decimal place.) ➀ 90.0% ➋ 90.9% ➂ 0.0% ➃ 2.0% 2.2%