Sample Test II Math 1107 DeMaio Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the indicated probability. 1) You are dealt a hand of three cards, one at a time. Find the probability that you get no black cards. A) 0.118 B) 0.013 C) 0.231 D) 0.414 E) 0.125 2) A study conducted at a certain college shows that 62% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. A) 0.200 B) 0.620 C) 0.908 D) 0.992 3) A sample of 4 different calculators is randomly selected from a group containing 38 that are defective and 23 that have no defects. What is the probability that all four of the calculators selected are defective? A) 0.1506 B) 8.3360 C) 0.1342 D) 0.1414 4) Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.327. Find the probability that in a given year it will not snow on January 1st in that town. A) 1.327 B) 3.058 C) 0.673 D) 0.486 5) If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap years. A) 31 1 B) C) 1 1 D) 365 12 31 365 1) 2) 3) 4) 5) 1
6) The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. 6) 12 48 95 34 189 9 47 75 40 171 60 184 303 173 720 Find the probability that the person was an attorney and retired before the age of 61. A) 0.518 B) 0.326 C) 0.067 D) 0.317 E) 0.083 7) A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable. A) 0.343 B) 2.1 C) 0.027 D) 0.429 8) The table below shows the soft drinks preferences of people in three age groups. cola root beer lemon-lime under 21 years of age 40 25 20 between 21 and 40 35 20 30 over 40 years of age 20 30 35 7) 8) If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age given that they drink root beer. A) 6 17 C) 5 17 B) 2 5 D) None of the above is correct. 2
9) The table below shows the soft drinks preferences of people in three age groups. cola root beer lemon-lime under 21 years of age 40 25 20 between 21 and 40 35 20 30 over 40 years of age 20 30 35 9) If one of the 255 subjects is randomly selected, find the probability that the person drinks root beer given that they are over 40. A) 2 6 B) 17 17 C) 2 5 D) None of the above is correct. 10) 100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected, find the probability that the person drives alone or cycles to work. 10) 1. Public transportation: 6 full time, 10 part time 2. Bicycle: 4 full time, 4 part time 3. Drive alone: 31 full time, 28 part time 4. Carpool: 10 full time, 7 part time A) 0.59 B) 0.67 C) 0.35 D) 0.39 11) A group of volunteers for a clinical trial consists of 81 women and 77 men. 18 of the women and 19 of the men have high blood pressure. If one of the volunteers is selected at random find the probability that the person has high blood pressure given that it is a woman. A) 0.234 B) 0.222 C) 0.513 D) 0.114 E) 0.486 12) A study conducted at a certain college shows that 61% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that 9 randomly selected graduates all find jobs in their chosen field within a year of graduating. A) 0.019 B) 0.012 C) 0.148 D) 5.490 11) 12) 3
Determine whether the events are disjoint and give a reason. 13) According to a survey conducted by an environmental organization, the probability that an eligible voter cares about environmental issues is 0.63, the probability that an eligible voter voted in the last election is 0.44 and the probability that an eligible voter both voted in the last election and cares about environmental issues is 0.30. Are caring about environmental issues and voting in the last election disjoint events? A) Yes, the probability that a voter cares about environmental issues is the same as the probability that a voter cares about environmental issues given that they voted in the last election. B) Yes, because P(C or V) = P(C) + P(V) C) Yes, the probability that a voter cares about environmental issues and voted in the last election is zero. D) Cannot be determined from the information given E) No, 30% both care about environmental issues and voted in the last election Solve the problem. 14) Many stores run "secret sales": Shoppers receive cards that determine how large a discount they get, but the percentage is revealed by scratching off that black stuff only after the purchase has been totaled at the cash register. The store is required to reveal (in the fine print) the distribution of discounts available. Determine whether the following probability assignment is legitimate. 13) 14) Probability of... 10% off 20% off 30% off 50% off 0.05 0.20 0.45 0.20 A) Legitimate B) Not legitimate 15) In a survey of American women who were asked to name their favorite color, 18% said blue, 15% said red, 15% said green, 12% said yellow, 13% said black, and the rest named another color. If you pick a survey participant at random, what is the probability that she named another color? A) 0.73 B) 0.24 C) 0.20 D) 0.27 E) 0.78 Determine whether the events are disjoint, independent, neither, or both. 16) In filling out a ballot for president, the events of voting for the Democratic candidate and voting for the Republican candidate A) Disjoint B) Independent C) Neither D) Both List the sample space and tell whether the events are equally likely. 17) Roll two dice; record the positive difference. A) {0, 1, 2, 3, 4, 5}, not equally likely B) {0, 1, 2, 3, 4, 5}, equally likely C) {0, 6}, not equally likely D) {1, 2, 3, 4, 5, 6}, equally likely E) {1, 2, 3, 4, 5, 6}, not equally likely Determine whether the events are mutally exclusive. 18) Read a book by Mark Twain. Read about Tom Sawyer. A) Yes B) No 15) 16) 17) 18) 4
Estimate the probability of the event. 19) Of 1262 people who came into a blood bank to give blood, 361 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure. A) 0.254 B) 0.205 C) 0.337 D) 0.286 Determine whether the events are independent and give a reason. 20) Shameel has a flight to catch on Monday morning. His father will give him a ride to the airport. If it rains, the traffic will be bad and the probability that he will miss his flight is 0.04. If it doesn't rain, the probability that he will miss his flight is 0.03. The probability that it will rain on Monday is 0.26. Are rain and Shameel missing his flight independent events? Explain. A) Yes, if it rains, he cannot both miss his flight and catch his flight B) No, it is possible for both things to happen P(rain and miss flight) = 0.26 œ 0.04. This is greater than zero. C) No, the probability of Shameel missing his flight depends on whether it rains. P(miss flight rain) = 0.04, P(miss flight no rain) = 0.03 D) Yes, because P(miss flight and rain) = P(miss flight) œ P(rain) E) Yes, the probability of Shameel missing his flight does not depend on whether it rains. P(miss flight rain) = P(miss flight no rain) = 0.04 Is Event B dependent or independent of Event A? 21) A: A mosquito lands on your arm. B: You get a mosquito bite. A) Dependent B) Independent Answer the question. 22) Which of the following cannot be a probability? 19) 20) 21) 22) A) 3 5 B) 2 3 C) 5 3 D) 1 2 Solve the problem. Round your answer, as needed. 23) Opinion-polling organizations contact their respondents by sampling random telephone numbers. Assume that interviewers can now reach about 77% of U.S. households, while the percentage of those contacted who agree to cooperate with the survey is 32%. Each household, of course, is independent of the others. What is the probability of failing to contact a household or of contacting the household but not getting them to agree to the interview? A) 0.407 B) 0.754 C) 0.156 D) 0.844 E) 0.476 24) A consumer organization estimates that 34% of the households in a particular community have one television set, 39% have two sets, and 18% have three or more sets. If two households are chosen at random, what is the probability that at least one has a television set? A) 0.992 B) 0.828 C) 0.008 D) 0.910 E) 0.164 23) 24) 5
Answer Key Testname: SAMPLE TEST 2 1) A 2) D 3) D 4) C 5) A 6) E 7) A 8) B 9) B 10) B 11) B 12) B 13) E 14) B 15) D 16) A 17) A 18) B 19) D 20) C 21) A 22) C 23) B 24) A 6