Name: ______

Date: ______

AP Statistics

Ch. 5 Practice Test

Multiple Choice

  1. An insurance company’s 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?
  1. 3%
  2. 8%
  3. 12%
  4. 13%
  5. 17%
  1. Which two events are most likely to be independent?
  1. being a senior; going to homeroom
  2. registering to vote; being left-handed
  3. having a car accident; have a learner’s license
  4. doing Statistics homework; making an A on the test
  5. having 3 inches of snow in the morning; being on time for school
  1. Choose one of the 50 states at random. What is the probability it begins with an M?
  1. 0.12
  2. 0.14
  3. 0.16
  4. 0.18
  5. 0.20
  1. Suppose that in a certain part of the world, in any 50-year period the probability of a major plague is 0.39, the probability of a major famine is 0.52, and the probability of both a plague and a famine is 0.15. What is the probability of a famine given that there is a plague?

a.0.240

b.0.288

c.0.370

d.0.385

e.0.760

Questions 5 – 9 refer to the following study: One thousand students at a city high school were classified both according to GPA and whether or not they consistently skipped classes.

<2.0 / 2.0 – 3.0 / > 3.0 / Total
Many skipped classes / 80 / 25 / 5 / 110
Few skipped classes / 175 / 450 / 265 / 890
Total / 255 / 475 / 270 / 1000
  1. What is the probability that a student has a GPA between 2.0 and 3.0?

a.0.025

b.0.227

c.0.450

d.0.475

e.0.506

  1. What is the probability that a student has a GPA under 2.0 and has skipped many classes?

a.0.080

b.0.281

c.0.285

d.0.314

e.0.727

  1. What is the probability that a student has a GPA under 2.0 or has skipped many classes?

a.0.080

b.0.281

c.0.285

d.0.314

e.0.727

  1. What is the probability that a student has a GPA under 2.0 given that he/she has skipped many classes?

a.0.080

b.0.281

c.0.285

d.0.314

e.0.727

  1. Are “GPA between 2.0 and 3.0” and “skipped few classes” independent?

a.No, because 0.42275 ≠ 0.506.

b.No, because 0.42275 ≠ 0.890

c.No, because 0.450 ≠ 0.42275

d.Yes, because of conditional probabilities.

e.Yes, because of the product rule.

Questions 10 – 13 refer to the following study: 90 students in Ms. Frailey’s classes were classified both according to grade and whether they openly admitted that Ms. Frailey was the best teacher in the whole wide world.

A – B / C – D / F / Total
Thinks Ms. Frailey is “Da Bomb!” / 23 / 12 / 3 / 38
Thinks Ms. Frailey ranks somewhere in the vicinity of Pepe Le Pu / 2 / 31 / 19 / 52
Total / 25 / 43 / 22 / 90
  1. What is the probability that a student has a grade of A – B?

a.0.133

b.0.278

c.0.365

d.0.744

e.0.833

  1. What is the probability that a student has a grade of a C – D and thinks Ms. Frailey is “Da Bomb?”

a. 0.133

b.0.278

c.0.365

d.0.744

e.0.833

  1. What is the probability that a student has a grade less than an A – B or thinks Ms. Frailey ranks somewhere in the vicinity of Pepe Le Pu?

a.0.133

b.0.278

c.0.365

d.0.744

e.0.833

  1. What is the probability that a student fails given that they think Ms. Frailey ranks somewhere in the vicinity of Pepe Le Pu?

a.0.133

b.0.278

c.0.365

d.0.744

e.0.833

  1. Consider the following table of ages of U.S. Senators:

Age (years)<40 40-49 50-59 60 – 69 70 -79 >79

Number of senators: 5 30 36 22 5 2

What is the probability that a senator is under 70 years old?

a.0.02

b.0.05

c.0.10

d.0.95

e.0.98

  1. Suppose that 2% of a clinic’s patients are known to have cancer. A blood test is developed that is positive in 98% of patients with cancer but is also positive in 3% of patients who do not have cancer. If a person who is chosen at random from the clinic’s patients is given the test it comes out positive, what is the probability that the person actually has cancer. (Hint: Use a tree diagram to help you solve this…)

a.0.02

b.0.40

c.0.50

d.0.60

e.0.98

  1. A computer technician notes that 40% of computers fail because of the hard drive. 25% because of the monitor, 20% because of a disk drive, and 15% because of the microprocessor. If the problem is not in the monitor, what is the probability that it is in the hard drive?

a.0.150

b.0.400

c.0.417

d.0.533

e.0.650

Free Response

  1. You are up for your annual job performance review. You estimate there’s a 30% chance you’ll get a promotion, a 40% chance of a raise, and a 20% chance of getting both a raise and a promotion.
  1. Find the probability that you get a raise or a promotion.
  1. Are getting a raise and getting a promotion independent events? Explain.
  1. Assume that 75% of the AP Statistics students studied for the Chapter 5 Test. If 40% of those who studied get an A, but only 10% of those who don’t study get an A, what is the probability that someone who gets an A actually studied?
  1. The judicial committee at a particular college consists of 2 administrators, 4 faculty, 4 seniors, 4 juniors, 2 sophomores, and 2 freshmen. Suppose one committee member is chosen at random. Find the probability:

a.That a student is selected

b.That a senior or junior is selected

c.That a nonstudent is selected

  1. A well-known paradox runs as follows: Suppose every couple continues having children until they have a boy and then they stop. What percentage of male births will result? No couple has more than one boy, while many can have numerous girls, so it appears that the population will become overwhelmingly female. Test this using a simulation. What conclusion do you reach? In looking at your simulation outcomes, what do you see is wrong with the reasoning above that led to the conclusion about an increasingly female population?