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Ch. 3 - Problems to look at Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) A coin is tossed. Find the probability that the result is heads. A) 0.5 B) 0.9 C) 0.1 Answer: A 1) D) 1 2) A single six-sided die is rolled. Find the probability of rolling a number less than 3. Answer: B 2) 3) A study of 1000 randomly selected flights of a major airline showed that 769 of the flights arrived on time. What is the probability of a flight arriving on time? Answer: D 231 1000 1000 769 A) B) C) D) 1000 231 769 1000 3) 4) The distribution of blood types for 100 Americans is listed in the table. If one donor is selected at random, find the probability of selecting a person with blood type A+. Answer: A 4) A) 0.25 Blood Type O+ Number 37 B) 0.333 O6 A+ 34 A) 0.34 A6 C) 0.1 B+ 10 B2 AB+ 4 B) 0.68 D) 0.5 AB1 C) 0.4 D) 0.45 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 5) Identify the sample space of the probability experiment: shooting a free throw in basketball. 5) S= {make the shot, miss the shot} 6) Identify the sample space of the probability experiment: recording the number of days it snowed in Cleveland in the month of January. 6) S={0,1,2,3,4,5,6,7,.......,31} 7) Identify the sample space of the probability experiment: rolling a single 12-sided die with sides numbered 1-12 S={1,2,3,4,5,6,7,8,9,10,11,12} 1 7) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning. 8) You roll a six-sided die. Event B is rolling an even number. Answer: A 8) A) 3; Not a simple event because it is an event that consists of more than a single outcome. B) 2; Not a simple event because it is an event that consists of more than a single outcome. C) 1; Simple event because it is an event that consists of a single outcome. D) 3; Simple event because the die is only rolled once. 9) You randomly select one card from a standard deck. Event B is selecting the ace of hearts. Answer: A 9) A) 1; Simple event because it is an event that consists of a single outcome. B) 4; Simple event because only one card is selected. C) 13; Not a simple event because it is an event that consists of more than a single outcome. D) 4; Not a simple event because it is an event that consists of more than a single outcome. Provide an appropriate response. 10) Which of the following cannot be a probability? 5 A) 0.001 B) 3 11) Rank the probabilities of 10%, A) 1 , 10%, 0.06 5 Answer: C C) -68 10) D) 0 1 , and 0.06 from the least likely to occur to the most likely to occur. 5 B) 0.06, 10%, 1 5 C) 0.06, 1 , 10% 5 12) Classify the events as dependent or independent. Events A and B where P(A) = 0.7, P(B) = 0.7, and P(A and B) = 0.49 A) dependent Answer: B D) 10%, 11) 1 , 0.06 5 Answer: B 12) Answer: B 13) B) independent 13) Classify the events as dependent or independent. Events A and B where P(A) = 0.8, P(B) = 0.1, and P(A and B) = 0.07 A) dependent B) independent 2 14) A group of students were asked if they carry a credit card. The responses are listed in the table. Answer: C Credit Card Not a Credit Card Class Carrier Carrier Total Freshman 17 43 60 Sophomore 28 12 40 Total 45 55 100 14) If a student is selected at random, find the probability that he or she owns a credit card given that the student is a sophomore. Round your answer to three decimal places. A) 0.622 B) 0.300 C) 0.700 D) 0.280 15) A group of students were asked if they carry a credit card. The responses are listed in the table. Answer: D Credit Card Not a Credit Card Class Carrier Carrier Total Freshman 10 50 60 Sophomore 20 20 40 Total 30 70 100 15) If a student is selected at random, find the probability that he or she is a sophomore and owns a credit card. Round your answers to three decimal places. A) 0.667 B) 0.750 C) 0.333 D) 0.200 16) You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten. Round your answer to three decimal places. Answer: B A) 0.250 B) 0.006 C) 0.994 16) D) 0.500 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 17) Find the probability of getting four consecutive aces when four cards are drawn without replacement from a standard deck of 52 playing cards. 17) =(4/52)+(3/52)+(2/52)+(1/52) =0.00000369 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 18) Decide if the events A and B are mutually exclusive or not mutually exclusive. A die is rolled. Answer: A A: The result is an odd number. B: The result is an even number. A) mutually exclusive B) not mutually exclusive 3 18) 19) Decide if the events A and B are mutually exclusive or not mutually exclusive, A die is rolled. Answer: A A: The result is a 3. B: The result is an odd number. A) not mutually exclusive 19) B) mutually exclusive 20) Decide if the events A and B are mutually exclusive or not mutually exclusive. A card is drawn from a standard deck of 52 playing cards. Answer: B A: The result is a 7. B: The result is a jack. A) not mutually exclusive 20) B) mutually exclusive 21) A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is an ace or a king. Answer: D 1 4 8 2 A) B) C) D) 13 13 13 13 21) 22) A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is an ace or a black card. Answer: C 15 29 7 4 A) B) C) D) 26 52 13 13 22) 23) The events A and B are mutually exclusive. If P(A) = 0.6 and P(B) = 0.2, what is P(A or B)?Answer: B 23) A) 0.12 B) 0.8 C) 0.4 D) 0 24) The table lists the smoking habits of a group of college students. 24) Sex Non-smoker Regular Smoker Heavy Smoker Total Man 135 70 5 210 Woman 187 21 15 223 Total 322 91 20 433 If a student is chosen at random, find the probability of getting someone who is a man or a non-smoker. Round your answer to three decimal places. Answer: D A) 0.950 B) 0.790 C) 0.942 D) 0.917 25) The events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.4, what is P(A and B)? Answer: C A) 0.12 B) 0.5 C) 0 4 D) 0.7 25) Solve the problem. 26) There are 3 balls in a hat; one with the number 2 on it, one with the number 4 on it, and one with the number 9 on it. You pick a ball from the hat at random and then you flip a coin. Using a tree diagram , obtain the sample space for the experiment. List the elements that make up the sample space. Answer: D A) 2 4 9 H, 2 4 9 T B) 2 H, 4 H, 9 H C) 2 H T, 4 H T, 9 H T D) 2 H, 2 T, 4 H, 4 T, 9 H, 9 T 27) Which of the following events are mutually exclusive? Answer: C 26) 27) A) being a college student and being a high school graduate B) being a steelworker and being a stamp collector C) being a mother and being an uncle D) living in Baltimore and working in Washington, D.C. E) none of these 28) Two events A and B are mutually exclusive if A) A Answer: D 28) B = U. B) A B = . C) A B = U. D) A B= . E) none of these 29) Two fair die are rolled. What is the probability that the numbers that appear are both 3? Answer: B 1 A) 3 B) 1 36 C) 1 2 D) 1 6 29) E) none of these 30) Let E and F are mutually exclusive and Pr(E) = 0.2 and Pr(F) = 0.6. Find Pr(E A) 0.12 B) 0 C) 1 D) 0.8 E) none of these 5 F). Answer: D 30) A basket contains five red balls, four white balls and three blue balls. Two balls are drawn, one after the other, with the first ball replaced before the second is drawn. 31) Find the probability of drawing two white balls. 1 A) 9 B) 4 1 = 12 3 C) 2 1 = 12 6 D) 2 9 Answer: A 31) E) none of these Solve the problem. 32) Two coins are tossed 20 times and the number of tails is observed. Outcome Frequency Answer: B 32) 2 tails 1 tail 0 tails 3 7 10 Compute the empirical probability that exactly one tail occurred. 1 7 17 A) B) C) 4 20 20 D) 1 2 Estimate the indicated probability. 33) The table shows the number of college students who prefer a given pizza topping. Answer: D toppings freshman sophomore junior senior cheese 10 15 26 21 meat 24 21 15 10 veggie 15 10 24 21 33) Determine the empirical probability that a junior prefers meat toppings. A) 0.071 B) 0.214 C) 0.320 D) 0.231 Find the probability. 34) A bag contains 2 red marbles, 4 blue marbles, and 8 green marbles. What is the probability of choosing a blue marble? Answer: B 2 2 1 4 A) B) C) D) 3 7 7 7 6 34) 35) Determine the probability that the spinner lands on white. A) 1 B) 1 4 C) 1 2 Answer: B D) 35) 1 3 36) A fair die is rolled. What is the probability of rolling an odd number or a number less than 3? Answer: A 2 1 5 A) B) C) D) 1 3 2 6 36) 37) A bag contains 8 red marbles, 2 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue? Answer: A 9 11 2 A) B) 9 C) D) 11 9 11 37) Solve the problem. 38) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd. Answer: A 1 1 A) 0 B) C) 1 D) 6 2 38) Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the probability. 39) The second marble is white given the first marble is blue. 3 3 3 A) B) C) 56 64 7 7 Answer: C 3 D) 8 39)