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M118 MIDTERM EXAMINATION FEBRUARY 23, 2008
printed Name: ______________________________________________
Signature: _________________________________________________
Instructor: ___________________ seat number: _____________
INSTRUCTIONS: This exam consists of 25 multiple-choice questions. Each question
has one correct answer choice. Indicate your answer choice for each question by
placing the appropriate CAPITAL letter in the appropriate space on this page. You
may write in the test as much as needed, but no credit is given for anything written
inside the exam itself. Only your answers on this cover page will be graded. No scrap
paper is allowed, and you may use only one-line or two-line scientific calculators.
Please keep this cover page attached to your exam. GOOD LUCK!
INDICATE ALL ANSWERS ON THIS PAGE, AND PLEASE USE CAPITAL LETTERS.
1) __________ 14) __________
2) __________ 15) __________
3) __________ 16) __________
4) __________ 17) __________
5) __________ 18) __________
6) __________ 19) __________
7) __________ 20) __________
8) __________ 21) __________
9) __________ 22) __________
10) _________ 23) __________
11) _________ 24) __________
12) _________ 25) __________
13) _________
SCORE: ____________
PROBLEM 01: Given the universal set U = { a, b, c, d, e, f, g, h, j }, with subsets A = { a, c, d, e, h }, and B = { b, d, e, f, g }, which
of the following represents the set A ∩ B’?
A) { a, b, c, f, g, h, j } B) { a, c, h } C) { d, e } D) { b, f, g } E) none of the above PROBLEM 02: Given a universal set U with two subsets, A and B, which of the following statements is ALWAYS true? A) (A’ ∩ B) ⊂ (A ∪ B)’ B) (A ∪ B) ⊂ (A ∩ B’ ) C) (A’ ∩ B) ⊂ (A ∩ B)’ D) (A ∩ B)’ ⊂ (A’ ∩ B’ ) E) none of the above PROBLEM 03: A sample space S has two independent events, A and B, with Pr[A] = 0.36 and Pr[ A’ ∩ B’ ] = 0.48. Which of the following represents Pr [ A ∩ B’ ]? A) 0. B) 0. C) 0. D) cannot be determined without more information E) none of the above PROBLEM 04: There are 3,000 students taking the M midterm exam this morning. Of these, 600 are juniors, 1,100 are business majors, and 300 are juniors majoring in business. How many of the students taking the exam are neither business majors nor juniors? A) 1, B) 2, C) 1, D) 1, E) none of the above PROBLEM 05: There are 540 students at a walk-in clinic, each of which has either the flu, a sinus infection, or bronchitis (no student has more than one of these illnesses). If the number of students with the flu is two times the number of students with bronchitis, and the number of students with a sinus infection is three times the number of students with the flu, how many of the 540 students have the flu? A) 60 B) 90 C) 180 D) 120
PROBLEM 11: On a particular day, the probability that it rains in Bloomington is 1/3. In addition, if it rains, the probability is 3/4 that 87-year-old Velma Watson will be involved in a car accident, whereas if it does not rain, the probability is only 1/4 that Velma will be involved in a car accident. If it is known that Velma was involved in a car accident on that day, what is the probability that it was raining in Bloomington? A) 1/ B) 3/ C) 3/ D) 1/ E) none of the above PROBLEM 12: Every time Bob Loblaw goes to the grocery store, there is a 30% chance that the store will be out of his favorite cereal. If he makes six trips to the store during a given month, what is the probability that the store will be out of his favorite cereal on one of those six trips to the store? A) 6·(0.3)^1 ·(0.7)^5 B) 6·(0.3)^5 ·(0.7)^1 C) (0.3)^1 ·(0.7)^5 D) 1·(0.3)^0 ·(0.7)^6 + 6·(0.3)^1 ·(0.7)^5 E) none of the above PROBLEM 13: A fair coin is tossed until a total of two Tails land up, or until a total of three Heads land up, whichever comes first. Find the expected number of tails tossed. A) 4/ B) 25/ C) 1 D) 2 E) none of the above PROBLEM 14: J-fed is to perform at three of the following five cities on his current concert tour: Atlanta, Baltimore, Cincinnati, Detroit, and Ellettsville. If he picks the three cities and the order they are to be visited randomly, what is the probability that he performs in both Cincinnati and Ellettsville, with the Cincinnati concert occurring sometime before the Ellettsville concert? A) 3/ B) 1/ C) 1/ D) 3/ E) none of the above PROBLEM 15: For three consecutive weeks, the Big Ten Player of the Week is either Eric Gordon or DJ White. If the selection each week is made by randomly choosing between the two players, and it is known that Eric Gordon is chosen at least once, what is the probability that he is chosen at most two times? A) 1/ B) 6/ C) 2/ D) 3/
PROBLEM 16: In a local restaurant, 40% of the customers were born in Indiana, 40% were born in Ohio, and 35% are IU students. In addition, 10% of the customers are IU students who were born in Indiana, and 20% are IU students who were born in Ohio. If one customer is randomly selected from the restaurant, and it is known that the customer was born in neither Indiana nor Ohio, what is the probability that the customer is an IU student? A) 1/ B) 1/ C) 1/ D) 0. E) none of the above PROBLEM 17: A random variable X takes four possible values, 0, 2, a, and b, where a and b are unknown numbers. If Pr[X = 0] = 0.2, Pr[X=2] = 0.4, Pr[X = a] = 0.3, E[X] = 2.8 and it is the case that a + b = 6, what is the missing value of a? A) -1. B) 5. C) 7. D) cannot be determined without more information E) none of the above PROBLEM 18: A dart thrower “randomly” throws darts at a dartboard. If the probability that the dart hits the dartboard on each throw is 0.40, what is the probability that at least one of the first two throws hits the dartboard? A) 0. B) 0. C) 0. D) 0. E) none of the above PROBLEM 19: A sample space S has in it two events, A and B, with Pr[A] = 0.5, Pr[ A | B ] = 0.8, and Pr[ B ] = 0.6. Which of the following represents Pr[ B | A’ ]? A) 0. B) 0. C) 0. D) 0. E) none of the above PROBLEM 20: A school Science Fair team will consist of two male students, two female students, and one “alternate”. The alternate can be of either sex. There are four males (including Ted) and five females (including Vanessa) trying out for the team. A Team Roster is a list
of the five students chosen,without mention of which one of the five
will be the alternate. If the five students are chosen randomly from
among the nine trying out, find the probability that the Team Roster contains both Ted and Vanessa. A) 8/ B) 2/ C) 2/ D) 3/
