AP Stats
Chap 14-15
Test Name __________________________________________ Pd __________
SECTION I
Directions: Solve each of the following problems.
1. At the track, a gambler bets on the wrong horse in a 10-horse field nine times in a row. Later,
when talking to a friend, he said he was confident that he would pick the winner the next
time, because he was "due to pick a winner." Comment on his reasoning.
A. When there are 10 horses in a race and he has chosen the wrong horse nine
times in a row, he statistically should pick a winner the next time.
B. This is false reasoning because there is no Law of Averages for independent events.
C. This is false reasoning because he doesn't appear to be lucky
D. If he doesn't pick the winning horse the next time, he will shortly after that.
E. None of the above
2. The plastic arrow on a spinner for a child's game stops rotating to point at a color that will determine
what happens next. Determine whether the following probability assignment is legitimate.
A. Legitimate B. Not legitimate
3. In abusiness class, 25% of the students have never taken a statistics class, 35% have taken only one
semester of a statistics class, and the rest have taken two or more semesters of statistics. The
professor randomly assigns students to groups of three to work on a project for the course. What is
the probability that the first groupmate you meet has studied at least 1 semester of statistics?
A. 0.75 B. 0.60 C. 0.65 D. 0.35 E. 0.40
4. An Imaginary Poll in January 2005 asked 1194 U.S. adults how likely they were to see a new movie
that was coming out in the summer. Here's how they responded:
Let's call someone who responded that they would definitely or probably see it a "likely viewer"
and the other two categories, "unlikely viewer." If we select two people at random from this
sample, what is the probability that neither is a likely viewer?
A. 0.601 B. 0.362 C. 0.097 D. 0.084 E. 0.159
5. Opinion-polling organizations contact their respondents by sampling random telephone numbers. Assume that interviewers can now reach about 71% of U.S. households, while the percentage of those contacted who agree to cooperate with the survey is 31%. 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. 0.800 B. 0.200 C. 0.780 D. 0.496 E. 0.510
6. In a blood testing procedure, blood samples from 5 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.11, what is the probability that the mixture will test positive?
A. 0.442 B. 1 C. 0.11 D. 0.0000161 E. 0.0121
7. You roll a fair die six times. What is the probability that you roll all 5's?
A. 1.2 B. 1 C. 0.833 D. 0.167 E. 0.00002
8. You roll a fair die three times. What is the probability that the numbers you roll are not all 2's?
A. 0.995 B. 0.833 C. 0.579 D. 0.421 E. 0.005
9. Which two events are most likely to be independent?
A. Getting an A in math, and getting an A in Physics.
B. Having a flat tire, and being late for school
C. Having a car accident, and having 3 inches of snow today
D. Having a driver's license, and having blue eyes
E. Being a senior, and leaving campus for lunch
10. A survey revealed that 34% of people are entertained by reading books, 47% are entertained by watching TV, and 19% are entertained by both books and TV. What is the probability that a person will be entertained by either books or TV?
A. 0.62 B. 1 C. 0.19 D. 0.60 E. 0.81
11. You draw a card at random from a standard deck of 52 cards. Find the probability that the card is a
diamond given that it is a queen.
A. 0.25 B. 0.077 C. 0.333 D. 0 E. 0.5
12. 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.
A. 0.121 B. 0.231 C. 0.450 D. 0.268 E. 0.523
13. A sample of 4 different calculators is randomly selected from a group containing 50 that are defective and 25 that have no defects. What is the probability that all four of the calculators selected are defective?
A. 0.189 B. 0.063 C. 0.182 D. 0.811 E. 0.198
14. A teacher designs a test so that 88% of students who study will pass and 12% of students who don't study will pass. 85% of students study for a test. What is the probability that a randomly selected student
passes?
A. 0.748 B. 0.766 C. 0.18 D. 0.88 E. 0.5
15. Melissa is looking for the perfect man. She claims that of the men at her college, 41% are smart, 32% are funny, and 20% are both smart and funny. If Melissa is right, what is the probability that a man chosen at random from her college is neither funny nor smart?
A. 0.47 B. 0.8 C. 0.27 D. 0 E. 0.67
SECTION II
PART A
Directions: Show all of your work for full credit!
16. Five multiple choice questions, each with four possible answers, appear on your history exam.
What is the probability that if you just guess, you
16a. get none of the questions correct?
16b. get all of the questions correct?
16c. get at least one of the questions wrong?
16d. get your first incorrect answer on the fourth question?
17&18. The Masterfoods company manufactures bags of Peanut Butter M&M’s. They report that they
make 10% each brown and red candies, and 20% each yellow, blue, and orange candies. The rest of the candies are green.
17. If you pick a Peanut Butter M&M at random, what is the probability that
17a. it is green?
17b. it is a primary color (red, yellow, or blue)?
17c. it is not orange?
18. If you pick four M&M’s in a row, what is the probability that
18a. they are all blue?
18b. none are green?
18c. at least one is red?
18d. the fourth one is the first one that is brown?
19. According to the American Pet Products Manufacturers Association (APPMA) 2003-2004
National Pet Owners Survey, 39% of U.S. households own at least one dog and 34% of U.S.
households own at least one cat. Assume that 60% of U.S. households own a cat or a dog.
19a. What is the probability that a randomly selected U.S. household owns neither a cat nor a
dog?
19b. What is the probability that a randomly selected U.S. household owns both a cat and a dog?
19c. What is the probability that a randomly selected U.S. household owns a cat if the
household has a dog?
SECTION II
PART B
Breakfast and Statistics
A survey of an introductory statistics class in Autumn 2003 asked students whether or not they
ate breakfast the morning of the survey. Results are as follows:
20a. What is the probability that a randomly selected student is female?
20b. What is the probability that a randomly selected student ate breakfast?
20c. What is the probability that a randomly selected student is a female who ate breakfast?
20d. What is the probability that a randomly selected student is female, given that the student ate
breakfast?
20e. What is the probability that a randomly selected student ate breakfast, given that the student is female?
20f. Does it appear that whether or not a student ate breakfast is independent of the student’s sex? Explain.