AP Statistics Probability Test A with Answers

AP Statistics Test A - Probability - Part IV (A) Name: Key Use the following information for questions 1-2: In an AP Stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth.   Forty-six percent of students eat breakfast and also floss their teeth.   1. What is the probability that a student from this class eats breakfast but does not floss their teeth? A) 9% B) 11% C) 34% D) 57% E) 91%   2. What is the probability that a student from this class eats breakfast or flosses their teeth? A) 9% B) 11% C) 34% D) 57% E) 91% P(B or F) = P(B) + P(F) - P(B and F) = .57 + .80 - .46 = .91 3. 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   that they are both juniors or both seniors? A) 0.395   B) 0.444 C) 0.506 D) 0.569 E) 0.722 4. A fair coin has come up "heads" 10 times in a row. The probability that the coin will come up heads on the next flip is: A) less than 50%, since "tails"   is due to come up. B) 50%. Independent C) greater than 50%, since it appears that we are in a streak of "heads." D) It cannot be determined. 5. According to the National Telecommunication and Information Administration, 56.5% of U.S. households owned a computer in 2001. What is the probability that of three randomly selected U.S. households at least one owned a computer in   2001? A) 18.0% B) 43.5% C) 56.5% D) 82.0% E) 91.8%   P(at least 1) = 1 - P(none) = 1 - (.435)^3 = .918 6. According to the National Telecommunication and Information Administration, 50.5% of U.S. households had Internet access in 2001. What is the probability that four randomly selected U.S. households all had Internet access in 2001?   A) 6.5% B) 12.6% C) 49.5% D) 50.5% E) 93.5%   (.505)^4 = .065 7. Which of these has a Binomial model? A) the number of people we survey until we find someone who has taken Statistics B) the number of people we survey until we find two people who have taken Statistics C) the number of people in a class of 25 who have taken Statistics D) the number of aces in a five-card Poker hand E) the number of sodas students drink per day   Geometric 1st success doesn't stop 8. Which of these has a Geometric model? A) the number of people we survey until we find someone who has taken Statistics B) the number of people we   survey until we find two people who have taken Statistics C) the number of people in a class of 25 who have taken Statistics D) the number of aces in a five-card Poker hand E) the number of sodas students drink per day   9. BatCo, a company that sells batteries, claims that 99.5% of their batteries are in working order. How many batteries would you expect to buy, on average, to find one that does not work?   A) 5 B) 100 C) 200 D) 995   E) 2000 E = 1/p = 1/.005 = 200 210. Some marathons allow two runners to "split" the marathon by each running a half marathon. Alice and Sharon plan to split a marathon. Alice's half-marathon times average 92 minutes with a standard deviation of 4 minutes, and Sharon's half-marathon times average 96 minutes with a standard deviation of 2 minutes. Assume that the women's half-marathon times are independent. The expected time for Alice and Sharon to complete a full marathon is 92+96-188 minutes, What is the standard deviation of their total time? A) 2 minutes B) 4.5 minutes C) 6 minutes D) 20 minutes E) It cannot be determined V42+22= V16+4 = 500 = 4.5 11. Passing the test Assume that 70% of teenagers who go to take the written drivers license test have studied for the test. Of those who study for the test, 95% pass; of those who do not study for the test, 60% pass. What is the probability that a teenager who passes the written drivers license test did not study for the test? Study 95 P 105 F 50 P(1P) ($7P) P(P) 13(.6) 17(95)+.3(.6) 12131) 3 Study F 12. Grades You believe that there is a 20% chance that you will earn an A in your English class, a 10% chance that you will earn an A in your Physics class, and a 5% chance that you will earn an A in both classes. a. Find the probability that you do not get an A in either English or Physics.