AP STATISTICS TEST #2 - REVIEW - Ch. 14 &15 Period:

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1 AP STATISTICS Name TEST #2 - REVIEW - Ch. 14 &15 Period: 1) The city council has 6 men and 3 women. If we randomly choose two of them to co-chair a committee, what is the probability these chairpersons are the same gender? 2) Five juniors and four seniors have applied for two open student council positions. School administrators have decided to pick the two new members randomly. What is the probability they are both juniors or both seniors? 3) Insurance company records indicate that 12% of all teenage drivers have been ticketed for speeding and 9% for going through a red light. If 4% have been ticketed for both, what is the probability that a teenage driver has been issued a ticket for speeding but not for running a red light? Determine whether the events are disjoint and give a reason. 4) Melissa is looking for the perfect man. She claims that at her college 27% of men are smart, 22% are funny, and 14% are both smart and funny. If Melissa is right, are being smart and being funny disjoint events? Determine whether the events are independent and give a reason. 5) According to a survey, 10% of students at a college are left handed, 47% are female, and 4.7% are both female and left handed. Is being left handed independent of gender? Explain. 6) A group of volunteers for a clinical trial consists of 86 women and 70 men. 18 of the women and 17 of the men have high blood pressure. Are high blood pressure and gender independent? Explain. 7) Melissa is looking for the perfect man. She claims that at her college 31% of men are smart, 24% are funny, and 14% are both smart and funny. If Melissa is right, are being smart and being funny independent events? 1

2 8) The contingency table below classifies a random sample of patients at a hospital by blood type and sex Are being blood type O and being blood type A independent events? SHOW why or why not. 2. Are being blood type O and being a male independent events? SHOW why or why not. 9) According to a survey conducted by an environmental organization, the probability that an eligible voter cares strongly about environmental issues is 0.58, the probability that an eligible voter votes regularly is 0.51 and the probability that an eligible voter both votes regularly and care strongly about environmental issues is What is the probability that someone who cares strongly about environmental issues votes regularly? 10) A group of volunteers for a clinical trial consists of 78 women and 71 men. 18 of the women and 22 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. 11) You are dealt a hand of three cards, one at a time. Find the probability that you have at least one queen. Solve the problem. 12) The probability that a student at a certain college is male is The probability that a student at that college has a job off campus is The probability that a student at the college is male and has a job off campus is If a student is chosen at random from the college, what is the probability that the student is male or has an off campus job? 2

3 Use a tree diagram to find the indicated probability. 13) 3.2% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 91.4% of those who have the disease will test positive. However 4.2% of those who do not have the disease will also test positive (false positives). What is the probability that a person who tests positive actually has the disease? 14) A company manufacturing electronic components for home entertainment systems buys electrical connectors from three suppliers. It buys 23% of the connectors from supplier A, 35% from supplier B, and 42% from supplier C. It finds that 1% of the connectors from supplier A are defective, 4% of the connectors from supplier B are defective, and 5% of the connectors from supplier C are defective. If a customer buys one of these components and finds that the connector is defective, what is the probability that it came from supplier B? 15) In one town in the Pacific Northwest, only 21% of days are sunny. A company's records indicate that on sunny days 2.3% of employees will call in sick.when it is not sunny, 1.1% of employees will call in sick. What percent of calls (where an employee calls in sick) occur on sunny days? 16) The sale bin in a clothing store contains an assortment of t-shirts in different sizes. There are 9 small, 7 medium, and 4 large shirts. Alan is looking for a large shirt. He starts grabbing shirts one at a time and checking the size. After he checks each shirt, he leaves it outside the bin. What is the probability that the first large shirt he finds is the third one he checks? 3

4 17) Applicants for a job first submit a written application. Based on the written applications, 27% of the applicants are invited for a first interview. Of those that have a first interview, 56% are rejected after the interview. What is the probability that a randomly selected applicant receives a first interview and is rejected after the interview? 18) You are dealt a hand of three cards, one at a time. Find the probability that your cards are all face cards. Use a tree diagram to find the indicated probability. 19) 3.3% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 94% of those who have the disease will test positive. However 4.4% of those who do not have the disease will also test positive (false positives). What is the probability that any given person will test positive? Round your answer to three decimal places if necessary. 20) In one town in the Pacific Northwest, only 23% of days are sunny. A company's records indicate that on sunny days 2.1% of employees will call in sick.when it is not sunny, 1.4% of employees will call in sick. What percent of employees call in sick on a randomly selected day? 21) The table shows the political affiliation of voters in one city and their positions on stronger gun control laws. Stronger Gun Control Favor Oppose Republican Democrat Other What is the probability that a voter who favors stronger gun control laws is a Republican? 4

5 Answer Key Testname: TEST AP STAT REVIEW 1) 1 2 2) ) 8% 4) No, 14% are both smart and funny 5) Yes, 10% of all students are left handed and 10% of female students are left handed. 6) No; P(High blood pressure) = P(High blood pressure Female) = These are not equal 7) No, overall 24% of men are funny, but among those who are smart 45.2% are funny. These are not equal. 8) No, the probability that a patient is blood type O is 0.47, but the probability that a person is blood type O given that they are blood type A is zero. No, the probability that a patient is blood type O is 0.47, but the probability that a person is blood type O given that they are male is Very close so only a slight relationship. 9) ) ) ) ) ) ) 35.7% 16) ) ) ) ) 1.561% 21)