Chapter 4 - Practice Problems 2

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1 Chapter - Practice Problems 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the indicated probability. 1) If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH THT TTH TTT. What is the probability of getting at least one head? 1) A) 3 B) D) 1 2) If two balanced die are rolled, what is the probability that the sum of the dice is or 12. 2) A) 1 9 B) D) 1 6 3) A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. 3) (Hint: There are 10 possible samples. List them all) A) 3 5 B) D) 7 10 ) A bag contains four chips of which one is red, one is blue, one is green, and one is yellow. A chip is selected at random from the bag and then replaced in the bag. A second chip is then selected at random. Make a list of the possible outcomes (for example RB represents the outcome red chip followed by blue chip) and use your list to determine the probability that the two chips selected are the same color. ) (Hint: There are 16 possible outcomes.) A) 1 8 B) D) 1 16 Estimate the probability of the event. 5) The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $100,000. Round your answers to the nearest tenth. 5) 112,000 12,000 92, ,000 96, , ,000 8,000 12, ,000 88, , ,000 96,000 12, , ,000 18,000 80, ,000 A) 0.6 B) D) 0.8 1

2 List the outcomes comprising the specified event. 6) When a quarter is tossed four times, 16 outcomes are possible. 6) HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes that comprise the following event. A = event exactly three tails are tossed A) HTTT, THTT, TTHT, TTTH, TTTT B) TTTH HTTT, THTT, TTHT, TTTH D) HTTT, THTT, TTTH 7) Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can be represented as follows. 7) ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be on the board. List the outcomes that comprise the following event. A = event that fewer than two men are selected A) ABC, ABD, ADE, BCE, BDE B) ABC, ABD, ACE, ADE, BCE, BDE ABC, ABD, ABE, ACE, ADE, BCE, BDE D) ACD, BCD, CDE Describe the specified event in words. 8) When a quarter is tossed four times, 16 outcomes are possible. The events A and B are defined as follows. 8) A = event exactly two tails are tossed B = event the first toss is heads Describe the event (A or B) in words. A) Event that the first toss is heads or the last two tosses are tails or both B) Event that exactly two tails are tossed and the first toss is heads Event that exactly two tails are tossed or the first toss is heads but not both D) Event that exactly two tails are tossed or the first toss is heads or both 2

3 9) The age distribution of students at a community college is given below. 9) Age (years) Number of students (f) Under Over A student from the community college is selected at random. The event A is defined as follows. A = event the student is between 26 and 35 inclusive. Describe the event (not A) in words. A) The event the student is at most 26 or at least 35 B) The event the student is under 26 or over 35 The event the student is under 26 and over 35 D) The event the student is over 35 Determine the number of outcomes that comprise the specified event. 10) The age distribution of students at a community college is given below. 10) Age (years) Number of students (f) Under Over A student from the community college is selected at random. The event A is defined as follows. A = event the student is between 26 and 35 inclusive. Determine the number of outcomes that comprise the event (not A). A) 527 B) D) 205 3

4 11) The number of hours needed by sixth grade students to complete a research project was recorded with the following results. 11) Hours Number of students (f) A student is selected at random. The events A and B are defined as follows. A = the event the student took between 6 and 9 hours inclusive B = the event the student took at most 7 hours Determine the number of outcomes that comprise the event (A or B). A) 6 B) D) 99 Determine whether the events are mutually exclusive. 12) The number of hours needed by sixth grade students to complete a research project was recorded with the following results. 12) Hours Number of students (f) A student is selected at random. The events A, B, and C are defined as follows. A = event the student took more than 9 hours B = event the student took less than 6 hours C = event the student took between 7 and 9 hours inclusive Is the collection of events A, B, and C mutually exclusive? A) Yes B) No

5 Find the indicated probability. 13) A bag contains 6 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? 13) A) 1 3 B) D) 1 6 1) A class consists of 59 women and 62 men. If a student is randomly selected, what is the probability that the student is a woman? 1) A) B) D) Find the indicated probability by using the special addition rule. 15) A relative frequency distribution is given below for the size of families in one U.S. city. 15) Size Relative frequency A family is selected at random. Find the probability that the size of the family is less than 5. Round approximations to three decimal places. A) B) D) ) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 5? A) 16 B) 8 D) ) 17) Two 6-sided dice are rolled. What is the probability that the sum of the numbers on the dice is 6 or 9? A) 1 B) 3 5 D) ) Find the indicated probability by using the complementation rule. 18) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years. 18) A) B) D)

6 19) The age distribution of students at a community college is given below. 19) Age (years) Number of students (f) Under Over A student from the community college is selected at random. Find the probability that the student is 21 years or over. Give your answer as a decimal rounded to three decimal places. A) B) D) Find the indicated probability. 20) The following contingency table provides a joint frequency distribution for the popular votes cast in the presidential election by region and political party. Data are in thousands, rounded to the nearest thousand. 20) A person who voted in the presidential election is selected at random. Compute the probability that the person selected voted Democrat. A) 0.2 B) D)

7 21) The table below shows the soft drink preferences of people in three age groups. 21) cola root beer lemon-lime under 21 years of age between 21 and over 0 years of age If one of the 255 subjects is randomly selected, find the probability that the person is over 0 and drinks cola. A) B) 17 D) None of the above is correct. 7

8 Answer Key Testname: CH SET 2 1) B 2) A 3) A ) C 5) B 6) C 7) C 8) D 9) B 10) C 11) D 12) A 13) C 1) B 15) C 16) B 17) D 18) A 19) D 20) C 21) A 8

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