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Study Guide: Statistics Chapter 4, Sections 1-3 (Probability) Name___________________________________ SHORT ANSWER. 1) What is the defini.on of sample space? 2) What is the difference between classical probability, empirical probability and subjec.ve probability? 3) If a sportscaster makes an educated guess as to how well a team will do this season, he is using what type of probability? 4) A child gets 20 heads out of 30 tosses of a coin. If he declared the chance of getting a head with that coin were 2/3, that would be an example of probability. 5) Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let A be the event that all three doors are in the same condition. List the outcomes of A. [Let "L" designate "locked" and U" designate "unlocked".] 6) Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let C be the event that at least two doors are in the same condition. List the outcomes of C. [Let "L" designate "locked" and U" designate "unlocked".] 7) If two dice are rolled one time, find the probability of getting a sum less than 5. 8) If a red suit is drawn from an ordinary deck of cards, what is the probability that the card is a diamond? 1 9) A 12-sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled. The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Find P(Less than 3). 10) For this year's mayoral election, voter dissatisfaction is very high. In a survey of 900 likely voters, 387 said they planned to write in an independent candidate rather than vote for the Democrat or Republican candidate for mayor. Estimate the percentage of voters who plan to write in an independent candidate? 11) In a poll of 497 university students, 248 said that they were opposed to legalizing marijuana. Estimate the percentage of students who oppose legalizing marijuana. 12) A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). List all the outcomes of the sample space. 13) A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that at least one answer is "A". [Hint: List all the outcomes of the sample space first.] 14) A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that neither of the answers is "B". [Hint: List all the outcomes of the sample space first.] 2 15) A coin is tossed 589 times and comes up heads 265 times. Use the Empirical Method to approximate the probability that the coin comes up heads. 16) So far this season, the university's football team has executed 140 running plays, 146 passing plays, and 18 "trick" plays. What is the probability that the team will not execute a trick play? 17) A Karate club consists of 34 persons holding a black belt (highest rating), 60 persons holding a brown belt (middle rating), and 87 persons holding a purple belt (lowest rating). What is the probability that a randomly-selected club member holds a black belt? 18) At a certain college, there were 700 science majors, 300 engineering majors, and 600 business majors. If one student was selected at random, the probability that the student is an engineering major is 19) A Karate club consists of 45 persons holding a black belt (highest rating), 64 persons holding a brown belt (middle rating), and 86 persons holding a purple belt (lowest rating). What is the probability that a randomly-selected club member holds a brown belt or a purple belt? 20) A jar contains four white marbles, five red marbles, and six black marbles. If a marble were selected at random, what is the probability that it is white or black? 21) In a fish tank, there are 15 goldfish, 8 angelfish, and 18 guppies. If a fish is selected at random, find the probability that it is an angelfish or a guppy. 3 22) A survey asked respondents to indicate their level of satisfaction with government spending. The results are show below. Response Very satisfied Somewhat satisfied Dissatisfied Total Number 600 3204 7105 10,909 Assume this is a simple random sample from a population. Use the Empirical Method to estimate the probability that a person is dissatisfied with government's spending? 23) A survey asked 33,592 homeowners how many pets they owned. The results were as followed: Number of Pets 0 1 2 3 4 or more Total Number of Homeowners 5271 11,960 8877 6071 1413 33,592 Assume this is a simple random sample of homeowners. Use the Empirical Method to estimate the probability that a homeowner has at least one pet. 24) There are 27,564 undergraduate students enrolled at a certain university. The age distribution is as follows: Age Range Number 13 - 14 3 15 - 17 436 18 - 22 11,514 23 - 30 9389 31 and up 6222 Total 27,564 What is the probability that a student is less than 18 years old? 4 25) An apartment building has the following distribution of apartments: 1 bedroom 2 bedroom 3 bedroom 1st floor 3 2 1 2nd floor 1 3 2 3rd floor 1 4 1 If an apartment is selected at random, what is the probability that it is not a 2 bedroom apartment on the 2nd floor? 26) The Statistics Club at Woodvale College sold college T-shirts as a fundraiser. The results of the sale are shown below. Choose one student at random. Find the probability that the student sold 11-15 T-shirts or less than 6 T-shirts. No. of t-shirts 0 1-5 6-10 11-15 16-20 20+ No. of club members 1 15 13 4 5 1 27) Let E be the event that a corn crop has an infestation of ear worms, and let B be the event that a corn crop has an infestation of corn borers. Suppose that P(E) = 0.19, P(B) = 0.11, and P(E and B) = 0.11. Find the probability that a corn crop has no corn borer infestation. 28) On a recent Saturday, a total of 1064 people visited a local library. Of these people, 250 were under age 10, 478 were aged 10–18, 163 were aged 19–30, and the rest were more than 30 years old. One person is sampled at random. What is the probability that the person is less than 19 years old? 5 29) On a recent Saturday, a total of 1065 people visited a local library. Of these people, 234 were under age 10, 489 were aged 10–18, 180 were aged 19–30, and the rest were more than 30 years old. One person is sampled at random. What is the probability that the person is more than 30 years old? 30) In a recent semester at a local university, 480 students enrolled in both General Chemistry and Calculus I. Of these students, 71 received an A in general chemistry, 57 received an A in calculus, and 34 received an A in both general chemistry and calculus. Find the probability that a randomly chosen student did not receive an A in general chemistry. 31) On a certain day, a cheese packaging facility packaged 510 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major and minor flaws. The following table presents the results. Major Flaw No Major Flaw Minor Flaw No Minor Flaw 23 38 75 374 Find the probability that randomly chosen cheese package has no major flaw. 32) If P(A) = 0.4, P(B) = 0.25, and A and B are mutually exclusive, find P(A or B). 33) Let A and B be events with P(A) = 0.8, P(B) = 0.7, and P(B|A) = 0.5. Find P(A and B). 6 34) A poll was taken of 14,681 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results were as follows. Education Level High School or Less Bachelor's Degree Master's Degree Ph.D. Total Male 3781 3615 585 57 8038 Female 2386 3715 497 45 6643 Total 6167 7330 1082 102 14,681 A person is selected at random. Compute the probability that the person is female and has a bachelor's degree. 35) A poll was taken of 14,437 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results were as follows. Education Level High School or Less Bachelor's Degree Master's Degree Ph.D. Total Male 3448 3042 528 71 7089 Female 2550 4304 451 43 7348 Total 5998 7346 979 114 14,437 A person is selected at random. Compute the probability that the person is male or has a Ph.D. 36) Let A and B be events with P(A) = 0.3, P(B) = 0.8. Assume that A and B are independent. Find P(A and B). 37) Let A and B be events with P(A) = 0.6, P(B) = 0.4, and P(A and B) = 0.24. Are A and B independent? 7 38) A fair die is rolled five times. What is the probability that it comes up 5 at least once? 39) A fast-food restaurant chain has 643 outlets in the United States. The following table categorizes them by city population and location and presents the number of outlets in each category. An outlet is chosen at random from the 643 to test market a new menu. Region Population of city Under 50,000 50,000 - 500,000 Over 500,000 NE 30 59 77 SE 33 50 126 SW NW 25 23 58 45 73 44 Given that the outlet is located in a city with a population under 50,000, what is the probability that it is in the Southwest? 40) A lot of 1000 components contains 300 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Find P(B|A). 41) A lot of 1000 components contains 350 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Find P(A). 8 42) According to popular belief, 80% of adults enjoy drinking beer. Choose a group of 2 adults at random. The probability that all of them enjoy drinking beer is: 43) Urn 1 contains 2 red balls and 6 black balls. Urn 2 contains 3 red balls and 5 black balls. Urn 3 contains 5 red balls and 2 black balls. If an urn is selected at random and a ball is drawn, find the probability it will be red. 44) A group of 12 male and 4 female students is talking about going out for pizza. If 50% of the male students actually go and 25% of the female students actually go, find the probability that a random student who goes out for pizza is female. 45) There are 2 first grade children, 4 second grade children, and 7 third grade children in a room. When choosing two children, what is the conditional probability of choosing a second grade child, given that either a first or a third grade child was chosen first? 9 Answer Key Testname: STUDY GUIDE CH 4 SEC 1_3 1) 2) 3) subjective probability 4) empirical 5) {LLL, UUU} 6) {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU} 1 7) 6 1 2 9) 1/6 10) 43% 11) 49.9% 12) {AA, AB, AC, BA, BB, BC, CA, CB, CC} 13) 5/9 14) 4/9 15) 0.45 16) 0.941 17) 0.188 3 18) 16 19) 0.769 20) 2/3 26 21) 41 22) 0.651 23) 0.843 24) 0.0159 5 25) 6 26) 0.5128 27) 0.89 28) 0.684 29) 0.152 30) 0.852 31) 0.88 32) 0.65 33) 0.4 34) 0.253 35) 0.494 36) 0.24 37) Yes 38) 0.5981 8) 10 Answer Key Testname: STUDY GUIDE CH 4 SEC 1_3 39) 0.225 40) 0.2993 41) 0.35 42) 0.640 43) 25 56 44) 1 7 45) 1 3 11