Determine whether the given events are disjoint. 1) Drawing a face card from a deck of cards and drawing a deuce A) Yes B) No

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1 Assignment Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the given events are disjoint. 1) Drawing a face card from a deck of cards and drawing a deuce 1) A) Yes B) No Identify the probability statement as empirical or not. ) The probability of a forest fire in Yellowstone National Park this year is.30. ) A) Not empirical B) Empirical 3) A single die is rolled one time. Find the probability of rolling an odd number or a number less than 3) 5. A) 5 6 B) 1 C) 1 3 ) Below is a table of data from a high school survey given to 500 parents. Find the probability that a ) randomly chosen parent would agree or strongly agree that the school is clean. Round your answer to the nearest hundredth. Strongly Disagree Disagree Neutral Agree Strongly Agree The school is safe The school is clean A).5 B).3 C) An experiment is conducted for which the sample space is S = {a, b, c, d}. Decide if the given probability assignment is possible for this experiment. 5) 5) Outcomes Probabilities a.50 b.6 c.11 d.13 Find the odds in favor of the indicated event. 6) Randomly drawing a number greater than from the cards pictured below. 6) A) to 1 B) 3 to 5 C) 3 to to 5 1

2 7) A survey of senior citizens at a doctor's office shows that 50% take blood pressure-lowering 7) medication, 8% take cholesterol-lowering medication, and % take both medications. What is the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication? Express the answer as a percentage A) 0% B) 96% C) 100% % Determine whether the given events are disjoint. 8) Being over 30 and being in college 8) A) Yes B) No Identify the probability statement as empirical or not. 9) The probability of an adult male's height being at least 6 feet is.5. 9) A) Empirical B) Not empirical 10) The probability that it will snow on December 5 in New York City is.0. 10) A) Empirical B) Not empirical 11) A family has five children. The probability of having a girl is 1. What is the probability of having 11) no girls? Round the answer to the fourth decimal place. A).065 B).0313 C) ) If two fair dice are rolled, find the probability that the roll is a double given that the sum is 11. 1) B) 1 C) 0 1 Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, green, and red marbles. Find the probability of the indicated result. 13) The second marble is red, given that the first marble is white. 13) B) C) ) One marble is white, and one marble is blue. 1) B) C) ) In a certain city, 1% of the people are business executives, and 9% of the business executives 15) drive Cadillacs. Assuming independent events, what is the probability of choosing a business executive who drives a Cadillac? Round the answer to the nearest hundredth. A).35 B).1 C).0.9

3 Assume that, at a certain college, 33% of all physics majors belong to ethnic minorities. Given a random sample of 10 physics majors, find the probability of the indicated event. Round your answer as appropriate. 16) No more than 6 belong to an ethnic minority. 16) A).913 B).9815 C) ) If two cards are drawn without replacement from an ordinary deck, find the probability that the 17) second card is a spade, given that the first card was a spade. A) B) 11 1 C) ) A family has five children. The probability of having a girl is 1. What is the probability of having 3 18) girls followed by boys? Round the answer to the fourth decimal place. A).65 B).315 C) ) If a single fair die is rolled, find the probability of a 5 given that the number rolled is odd. 19) A) 1 B) 1 6 C) Use the given table to find the indicated probability. 0) The following table contains data from a study of two airlines which fly to Smalltown, USA. 0) Number of flights arrived on time Number of flights arrived late Podunk Airlines 33 6 Upstate Airlines 3 5 P(flight arrived on time flight was on Upstate Airlines)? A) 11 B) C) 3 87 None of the above Express the answer as a percentage. 1) A coin is biased to show 3% heads and 57% tails. The coin is tossed twice. What is the probability 1) that the coin turns up heads once and tails once? A).51% B) 3% C) 57% 9.0% Provide an appropriate response. ) Can an event E for a sample space S contain an outcome that is not in S? ) 3

4 The table shows, for some particular year, a listing of several income levels and, for each level, the proportion of the population in the level and the probability that a person in that level bought a new car during the year. Given that one of the people who bought a new car during that year is randomly selected, find the probability that that person was in the indicated income category. Round your answer to the nearest hundredth. Income level Proportion of population Probability that bought a new car $ %.0 $ %.03 $10,000-1,999 5.%.06 $15,000-19, %.07 $0,000 -,999 9.%.09 $5,000-9, %.10 $30,000-3, %.11 $35,000-39, %.13 $0,000-9, %.15 $50,000 and over 1.7%.19 3) $50,000 and over 3) A). B). C).5.8 Express the answer as a percentage. ) 56% of the workers at Motor Works are female, while 59% of the workers at City Bank are female. If ) one of these companies is selected at random (assume a chance for each), and then a worker is selected at random, what is the probability that the worker will be female? A) 59% B) 3% C) 57.5% 56% Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary. 5) For two events M and N, P(M) =.1, P(N M) =.6, and P(N M') =.. Find P(M N). 5) A).86 B) 1.0 C) 0.1

5 The table shows, for some particular year, a listing of several income levels and, for each level, the proportion of the population in the level and the probability that a person in that level bought a new car during the year. Given that one of the people who bought a new car during that year is randomly selected, find the probability that that person was in the indicated income category. Round your answer to the nearest hundredth. Income level Proportion of population Probability that bought a new car $ %.0 $ %.03 $10,000-1,999 5.%.06 $15,000-19, %.07 $0,000 -,999 9.%.09 $5,000-9, %.10 $30,000-3, %.11 $35,000-39, %.13 $0,000-9, %.15 $50,000 and over 1.7%.19 6) $10,000 - $1,999 6) A).06 B).05 C).0.03 Provide an appropriate response. 7) 7) P(R') P(T R') Is P(R' T) = P(R) P(T R) + P(R') P(T R') a valid alternative form of Bayes' theorem (special case)? 8) Given that a student correctly uses the following form of Bayes' theorem, 8) P(R1 T) = P(T R1)P(R1) P(T R1)P(R1) + P(T R)P(R) + P(T R3)P(R3), make a precise statement about the value of P(R1 R R3). A) P = 1 B) 0 < P < 1 C) 0 P 1 P = 0 Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary. 9) For mutually exclusive events X1, X, and X3, let P(X1) =.38, P(X) =.35, and P(X3) =.7. Also, 9) P(Y X1) =.0, P(Y X) =.30 and P(Y X3) =.60. Find P(X3 Y). A).6 B).39 C) ) For mutually exclusive events X1, X, and X3, let P(X1) =.31, P(X) =.16, and P(X3) =.53. Also, 30) P(Y X1) =.0, P(Y X) =.30, and P(Y X3) =.60. Find P(X Y). A).0 B).10 C)

Math 235 Final Exam Practice test. Name

Math 235 Final Exam Practice test Name Use the Gauss-Jordan method to solve the system of equations. 1) x + y + z = -1 x - y + 3z = -7 4x + y + z = -7 A) (-1, -2, 2) B) (-2, 2, -1) C)(-1, 2, -2) D) No