University of Connecticut Department of Mathematics

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1 University of Connecticut Department of Mathematics Math 070Q Exam A Fall 07 Name: TA Name: Discussion: Read This First! This is a closed notes, closed book exam. You cannot receive aid on this exam from anyone else - No sharing of calculators! Make sure your exam has 0 questions and an answer sheet. Only scientific calculators are allowed on this exam. For each question, be sure to indicate your answer by both writing it in the table provided at the end and circling your answer choice as well. If we cannot determine your final answer, you may not receive any credit. Unless otherwise stated you must show work on every question to receive credit! This may consist of written work, an explanation of your thought process, etc. If part of the solution is written outside the space provided, then clearly indicate this. If you finish this exam early, check all your answers before handing in your copy. Once a copy is handed in, it cannot be taken back. Two pages of scratch paper have been attached to your answer sheets.

2 . Jackson and Charlie are out trick-or-treatiing. In Jackson s bag there are Snickers bars and Hershey bars. In Charlie s bucket there are Snickers bars and Hershey bar. Jackson, feeling generous, randomly takes one of his candy bars and puts it in Charlie s bucket. Charlie then randomly selects a bar from his own bucket to eat. If Charlie selects a Snickers bar, what is the probability that Jackson gave him a Hershey bar? 8 7. A coin is flipped 8 times in succession. In how many ways can at least two heads occur? How many subsets does the set {a, b, c} have? 8 6. You and your friends ( people in total) are throwing a party. Three of you are going to the Dairy Bar to get ice cream, two of you are going to get soda, and one of you is going to get party hats. In how many ways can this be done? 9, 7,70 6. Which of these denote the empty set? { } {} Both and

3 6. If A and B are sets and A B = A B then which must be true? A = A = B A = A B None of the above. 7. A student at UCONN has three exams on one day: English, biology, and mathematics. The student has a 0% chance of passing the English exam, a % chance of passing biology, and an 80% chance of passing math. What is the probability that the student passes exactly two of the exams? 7 8. If A, B and C are sets, which of the following are equal to A (B C)? (A B) (A C) (A B) C A (B C) None of the above. 9. The members of the UConn Math Club must select a president, a vice president, a treasurer, and a secretary. How many ways can this be done? (You do not need to show work on this problem.) 79,00,600 9, If a pair of fair six-sided dice are tossed, what is the probability of obtaining a sum of 6?

4 . An oil company estimates that only oil wells in 0 will yield commercial quantities of oil. Assume that successful drilled wells represent independent events. If wells are drilled, find the probability of obtaining a commercially successful well exactly times. Round your answer to decimals places Suppose a basketball player misses / of all free throws he shoots. If he shoots 8 free throws, what is the probability that he makes at least 6 of them? Round your answer to decimals places Four couples go out to see a movie. They all want to sit in the same row. How many ways can everyone be seated if each couple wants to sit together? Let E be the event that the life a certain light bulb is at least 00 hours, F be the event that the life is between 00 and 00 hours, and G be the event that the life is more than 00 hours. How is G related to E and F? F = E G F = E G F = E G C F = E C G. How many ways can you have a three of a kind poker hand?(a three of a kind consists of three cards of the same value and two cards with values different from the three cards and different from each other. Example: AAAQ.),78 09,8,9

5 6. A fair, 8-sided die (with the numbers through 8 on its faces) is rolled and the top number is observed. What is the probability that the number is even if it is known that the number is at most a? 8 7. In a survey of 00 people, a pet food manufacturer found that 00 owned a dog but not a cat, 0 owned a cat but not a dog, and 00 owned neither a cat nor a dog. How many owned a dog? In a group of 8 friends there are 6 Patriots fans and NY Giants fans. Four of the friends are randomly chosen and are given tickets to go to a football game together. What is the probability that all are Patriots fans? If a fair six-sided die is tossed and the top number is noted, what is the sample space? {,,,,, 6} {,, } {,, 6},,,,, 6 0. Suppose E and F are two disjoint events in a sample S with P (E) = 0. and P (F ) = 0.. Which of the following is equal to P ((E F ) C )?

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