AP Statistics: Probability Review



AP Statistics: Probability Review Name_______________________

1. Which of the following events are mutually exclusive?

X = the sum of two dice is 7

Y = the flip of a coin is a head

Z = the sum of two dice is 11

A) X and Y D) X, Y, Z

B) Y and Z E) no pair is mutually exclusive

C) X and Z

2. Identify why this assignment of probabilities cannot be legitimate:

P(A) = .4, P(B) = .3, P(A and B) = .5

A) A and B are not given as mutually exclusive events.

B) A and B are not given as independent events.

C) P(A|B) is not known.

D) P(A and B) cannot be greater than either P(A) or P(B).

E) The assignment is legitimate.

For problems 3 and 4:

P(A) = 0.5 P(B) = 0.6 P(A and B) = 0.1

3. P(A|B) = ?

A) 0.3 C) 1/6

B) 0.2 D) cannot be determined

4. We may conclude that:

A) A and B are independent

B) A and B are disjoint

C) either A or B always occurs

D) none of the above

5. P(A) = 0.3 P(B) = 0.4

If A and B are independent, we may conclude that:

A) P(A and B) = 0.12

B) P(A|B) = 0.3

C) P(B|A) = 0.4

D) All of the above

6. P(A) = 0.8 P(B|A) = 0.5

The probability that both A and B occur is:

A) 0.3 B) 0.4

C) 0.8 D) cannot be determined

For questions 7 and 8: The following table displays the results of a sample of a 99 subjects in which each person indicated his or her favorite sport of three listed. The data are organized by favorite sport and age group.

|Age |Football |Baseball |Soccer |

|Over 40 |15 |8 |7 |

|Between 20 and 40 |20 |11 |15 |

|Under 20 |8 |7 |8 |

7. What is the probability that a person chosen at random will be under 20 and favor baseball?

A) 7/26

B) 7/99

C) 26/99

D) 7/23

E) none of these

8. What is the probability that a person favors baseball given that he/she is under 20?

A) 7/26

B) 7/99

C) 26/99

D) 7/23

E) none of these

9. A manufacturing company has three suppliers for parts for its assembly line. The proportions of parts from suppliers A, B, and C are .4, .3, and .3 respectively. The proportion of defective parts from suppliers A, B, and C are .03, .05, and .02 respectively. What is the probability that a defective part, chosen at random, came from supplier A?

A) .182

B) .364

C) .456

D) .818

E) none of these

10. If the probability of a certain team winning is ¾, what is the probability that this team will win the first 3 games and lose the fourth?

A) 3/256 D) 81/256

B) 9/256 E) 27/256

C) 1/256

11. In a school, the probability that a student takes physics is .87 and the probability that a student takes calculus is .62. If every student takes at least one of these courses, what is the probability that a student takes both physics and calculus?

A) .42 D) .47

B) .43 E) .49

C) .45

AP Statistics: Probability Review (cont.) Name_______________________

12. If P(A) = .2 and P(B) = .1, what is P(A U B) if A and B are independent?

A) .02

B) .28

C) .30

D) .32

E) There is insufficient information to answer this question.

13. Suppose that, for any given year, the probabilities that the stock market declines, that women’s hemlines are lower, and that both events occur are, respectively, .4, .35, and .3. Are the two events independent?

A) Yes, because (.4)(.35) ≠ .3

B) No, because (.4)(.35) ≠ .3

C) Yes, because .4 > .35 > .3

D) No, because .5(.3 + .4) = .35

E) There is insufficient information to answer this question.

14. Suppose that, in a certain part of the world, in any 50-year period the probability of a major plague is .39, the probability of a major famine is .52, and the probability of both a plague and a famine is .15. What is the probability of a famine given that there is a plague?

A) .240

B) .288

C) .370

D) .385

E) .760

For questions 15-19: One thousand students at a city high school were classified both according to GPA and whether or not they consistently skipped classes.

| |3.0 |

| | |2.0-3.0 | |

|Skipped many classes |80 |25 |5 |

|Skipped few classes |175 |450 |265 |

15. What is the probability that a student has a GPA between 2.0 and 3.0?

A. .025 D. .475

B. .227 E. .506

C. .450

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

A. .080 D. .314

B. .281 E. .727

C. .285

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

A. .080 D. .314

B. .281 E. .727

C. .285

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

A. .080 D. .314

B. .281 E. .727

C. .285

19. Are “GPA between 2.0 and3.0” and “skipped few classes” independent?

A. No, because .475 ≠ .506

B. No, because .475 ≠ .890

C. No, because .450 ≠ .475

D. Yes, because of conditional probabilities

E. Yes, because of the product rule

Free Response:

1. Andrew is 55, and the probability that he will be alive in 10 years is .72. Ellen is 35, and the probability that she will be alive in 10 years is .92. Assuming that the life span of one will have no effect on the life span of the other, what is the probability that they will both be alive in 10 years?

2. A quality control procedure for testing Ready-Flash bulbs consists of drawing two bulbs at random from each lot of 100 without replacing the first. Find the probability that both bulbs are defective if the lot contains 10 defective flash bulbs.

3. At Hopewell Electronics, all 140 employees were asked about their political affiliation. The employees were grouped by type of work, as executives or production workers. The results are shown below.

Employee Type and Political Affiliation

Political Affiliation

|Type of |Democrat |Republican |Independent |Row Total |

|Employee |D |R |I | |

|Executive (E) |5 |34 |9 |48 |

|Production |63 |21 |8 |92 |

|Worker (PW) | | | | |

|Column Total |68 |55 |17 |140 |

a) Compute P(D) and P(E).

b) Compute P(D|E).

c) Are the events D and E independent?

d) Compute P(D and E).

e) Compute P(D or E).

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