AP Statistics	Name ________________________

Introduction to Probability, chapter 6	Partner _______________________

During this unit of study you will complete 5 guided labs to develop, practice, and apply concepts related to the study of probability. You are expected to work collaboratively with your partner during each class to develop concepts. You are expected to take notes on each of the 5 labs, assess and clarify your understanding, ask questions of your teacher as needed, and to complete the homework problems associated with each lab. You are expected to take responsibility for learning the concepts in this unit.

You will act as a flexible, self-directed learner. Specifically, you will

Manage your behavior so that you remain focused

Plan and budget time to meet the daily deadlines

Take ownership of your work and your own actions

Prioritize, plan, and manage work to achieve the intended results in a timely manner

Assess your own work in order to identify areas of strength and weakness

You will act as a collaborative partner in class. Specifically, you will

Understand and commit to the goals of this unit of study

Positively interact with my partner and others in class

Assume shared responsibility for collaborative work, and value the individual contributions made by my partner and others in class

Provide constructive feedback to my partner and others

After concluding the 5 computer-based lessons we will have a review day in class followed by a partner quiz. You will be graded on the completion of all of the problems in this packet as well as your daily level of participation. Specifically, you will be graded on how you attend to the behaviors listed above. Work intently to develop each of the concepts in this unit of study and ask for help when you need it.

AP Statistics	Name ________________________

Probability Homework	Partner’s Name ______________period _____

Lesson One: Practice and Homework Exercises

1. Choose a new car or light truck at random and note its color. Here are the probabilities of the most popular colors for vehicles in North America.

Color:	Silver	White	Black	Green	Blue	Red

Probability:	0.176	0.172	0.113	0.089	0.088	0.067

a) What is the probability that the vehicle you choose has any color other than the six listed?

b) What is the probability that a randomly chosen vehicle is either silver or white?

c) Choose two vehicles at random. What is the probability that both are either silver or white?

2. Roll 2 balanced die. The chart below represents the different outcomes.

Make a probability distribution where the x represents a certain sum.

1 1	2 1	3 1	4 1	5 1	6 1
1 2	2 2	3 2	4 2	5 2	6 2
1 3	2 3	3 3	4 3	5 3	6 3
1 4	2 4	3 4	4 4	5 4	6 4
1 5	2 5	3 5	4 5	5 5	6 5
1 6	2 6	3 6	4 6	5 6	6 6

x	2	3	4	5	6	7	8	9	10	11	12
P (x)

Find the probability of rolling doubles; find the probability of NOT rolling doubles.

What is the probability of rolling a 7 or an 11? Of rolling a 2, 3, or 12?

3. Consider the events listed below and a fair deck of cards.

Let	C = the event the card selected is a heart

D = the event the card selected is a face card

E = the event the card selected is an ace

G = the event the card selected is a 10 or jack

Which of the following are mutually exclusive (disjoint)? Explain you choice.

C and D

C and E

D and E

4. A couple plans to have three children. State the sample space then find the probability of having

a) all boys

all girls

two boys or two girls

at least one child of each sex (What is the complement of this event?)

5. Complements are often useful for calculating probabilities. Consider again rolling two fair dice. Use the idea of a complement to find each of the following.

(See table in #2)

(a) P (sum is not 3)

(b) P (sum is 5 or greater)

(c) P (sum is not equal to 3 or 7)

(d) P (sum is 10 or less)

(e) P (sum is greater than 2)

6. Four houses in a neighborhood have the same model of garage door opener. Each opener has 4096 possible transmitter codes. What is the probability that at least two of the four houses have the same code?

7. You are taking a multiple-choice test about a topic you are unfamiliar with so you have decided to guess randomly. There are 10 questions and each has four possible answers. What is the probability that you get at least one correct?

8. Screening large numbers of blood samples uses an enzyme immunoassay (EAI) test that detects antibodies to the virus. Samples that test positive are retested using a more accurate “western blots” test. Applied to people who have no HIV antibodies, EIA has a probability of about 0.006 of producing a false positive. If the 140 employees of a medical clinic are tested and all 140 are in fact free of HIV antibodies, what is the probability that at least one false positive will occur?

Lesson Two: Practice and Homework Exercises

9. 162 students are receiving awards at an awards banquet. 48 receive math awards, 78 receive English awards, and 14 receive both Math and English awards. What is the probability that a randomly chosen student has won an award for English or Math?

10. The probability of rain on Saturday or Sunday is given as 0.5. The probability of rain on Saturday is 0.2 and the probability of rain on Sunday is 0.4. What is the probability that it will rain on both Saturday and Sunday?

11. Let	A = the event the card selected is the king of hearts

B = the event the card selected is a king

C = the event the card selected is a heart

D = the event the card selected is a face card

Find the probability of selecting the following in a regular 52 deck of playing cards:

a) Not D

B and C

B or C

C and D

Find the probability of selecting 2 face cards with and then without replacement.

12. Winning Contracts: Consolidated Builders has bid on two large construction projects. The company president believes that the probability of winning the first contract (event A) is .6, that the probability of winning the second (event B) is .5, and that the joint probability of winning both jobs (event (A and B)) is .3. Draw a Venn diagram that illustrates the relation between events A and B and then find the probabilities below.

a) What is the probability that Consolidated wins at least one of the jobs?

b) Consolidated wins both jobs?

c) Consolidated wins the first job but not the second?

d) Consolidated does not win the first job but does win the second?

e) Consolidated does not win either job?

13. In a statistics class there are 18 juniors and 10 seniors; 6 of the seniors are females, and 12 of the juniors are males. Organize this information in a table. If a student is selected at random, find the probability of selecting:

a junior or a female

a senior or a female

a junior or a senior

a male and senior (so male senior)

14. Blood Bank: Refer to the accompanying diagram, which describes the blood groups and Rh factor of 100 people, based on data from the Greater New York Blood Program. In each case assume that 1 of the 100 subjects is randomly chosen and find the indicated probabilities.

P (group A)	Group B

8 RH+

P (type Rh -)	2 RH-

Group AB	4 RH+

P (group A or Rh-)	Group A 35 RH+ 1 RH-

5 RH -

P (group A or group B)

P (type Rh+)	39 RH+

6 RH-

P (group B or Rh+)

Group O

P (group AB or type Rh-)

P (group A or group O or type Rh+)

15. Common sources of caffeine are coffee, tea, and cola drinks. Suppose that

55% of adults drink coffee

25% of adults drink tea

45% of adults drink cola

and also that

15% drink both coffee and tea

5% drink all three beverages

25% drink both coffee and cola

5% drink only tea

Draw a Venn diagram marked with this information.

a)What percent of adults drink only cola?

b) What percent drink none of these beverages?

Lesson Three Practice and Homework Exercises

16. A study of hunting injuries and the wearing of “hunter orange” clothing showed that among 123 hunters injured when mistaken for game, 6 were wearing orange (based on data from the Centers for Disease Control). If a follow-up study begins with the random selection of hunters from this sample of 123, find the probability that the first two selected hunters were both wearing orange if

a) Selection is made with replacement

b) Selection is made without replacement

c) Which makes more sense in this case, selection with or without replacement?

17. A statistics teacher gives a surprise quiz consisting of 10 true or false questions and she states that passing requires at least 7 correct answers. Assume that an unprepared student adopts the questionable strategy of guessing for each answer.

a) Find the probability that the first 7 responses are correct and the last 3 are wrong.

b) Is the answer from part (a) equal to the probability of passing? Why or why not?

18. Make a Venn diagram for the following situation and answer the questions below. A recent poll states that 48% of US teenagers had read Harry Potter and the Half Blood Prince, 58% had seen the movie and that 22% both read the book and saw the movie. Find the probability that a randomly selected US teenager

a) Read the book but had not seen the movie

b) Has read the book given they have seen the movie

c) Has seen the movie given they have read the book

d) Has neither read the book nor seen the movie

19. Buying From Japan: Functional Robotics Corporation buys electrical controllers from a Japanese supplier. The company’s treasurer thinks that there is a 0.4 probability that the dollar will fall in value against the Japanese yen in the next month. The treasurer also believes that if the dollar falls there is probability 0.8 that the supplier will demand renegotiation of the contact. What is the probability the treasurer assigns to the event that the dollar falls and the supplier demands renegotiation? Let A be the event that the dollar falls and B be the event that the supplier demands renegotiation. Use the formula for conditional probability.

20. Refer back to the Harry Potter problem. Are the events “reading Harry Potter and the Half Blood Prince” and “seeing the movie Harry Potter and the Half Blood Prince” independent event? Justify your reasoning mathematically.

21. Choose an employed person at random. Let A be the event that the person chosen is a woman, and B the event that the person holds a managerial or professional job. Government data tell us that P (A) = 0.46 and that the probability of managerial and professional jobs among women is P (B │ A ) = 0.32. Find the probability that a randomly chosen employed person is a woman holding a managerial or professional position. That is, find P (A and B).

22. A student misses many classes because of malfunctioning alarm clocks. Instead of using one alarm clock, he decides to use three. What is the probability that at lease one of his alarm clocks works correctly if each individual alarm clock has a 99% chance of working correctly? Are three alarm clocks really better that one?

23. Here are the counts (in thousands) of earned degrees in the United States in a recent year, classified by level and by gender of the degree recipient:

BACHELOR	MASTERS	PROFESSIONAL	DOCTORATE	TOTAL
FEMALE	616	194	30	16	856
MALE	529	171	44	26	770
TOTAL	1145	365	74	42	1626

If you choose a degree recipient at random, what is the probability that the person you choose is a woman?

What is the probability that a randomly chosen degree recipient is a man?

What is the conditional probability that you choose a woman, given that the person chosen received a professional degree?

What is the conditional probability that the person chosen received a bachelor’s degree, given that he is a man?

Are the events “choose a woman” and “choose a professional degree recipient” independent?

Use the multiplication rule to find the probability of choosing a male bachelor’s degree recipient.

Confirm your answer to (f) by finding the probability of choosing a male bachelor’s degree recipient from the table of counts above.

Lesson Four: Practice and Homework

24. According to the Heart Association, 8% have heart disease. The probability that one tests positive when you have heart disease is 96%. It is also known that 7% will test positive when they don’t actually have heart disease. What is the probability that a person actually has heart disease if they test positive? Make a tree diagram.

25. Pregnancy Tests: At a particular clinic, 99 pregnancy tests were conducted. Of the 99 women, 86% are in fact pregnant. Of the pregnant women, 94% got a positive test result. Of the non-pregnant women, 21% also got a positive test result.

a) Find the probability that a randomly chosen woman got a positive test result.

b) Find the probability that a randomly chosen woman is pregnant and got a negative result.

c) Find the probability that a randomly chosen woman is not pregnant and she got a positive result.

d) Find the probability that a randomly chosen woman is not pregnant given she got a positive test result.

Lesson Five: Practice and Homework

26. A classroom has 24 seats and 24 students. Assuming the seats are not moved, how many different seating arrangements are possible?

27. How many distinguishable permutations are there of the word CONNECTICUT?

28. There are six roles to be assigned for a school play. In how many ways can the roles be assigned if 9 people audition? If 6 people audition?

29. Eight members of a school marching band are auditioning for 3 drum major positions. In how may ways can students be chosen to be drum majors?

30. There are 10 novels on the summer reading list. Students are required to read three of them. In how many ways can you choose which books to read?

31. The Board of Trustees for a local charity has 9 members. Each year, they elect a 3-person committee to oversee fundraising. They also elect a 3-person advisory council consisting of a chairperson, vice chairperson, and recording secretary.

a) How many different 3-person fundraising committees are there?

b) How many different advisory council committees are there?

(Hint, which of these is represented by a permutation and which by a combination? Does order matter or not?)

Answer Key

1. a) .295, b) .348, c) .06056	16. a) .0024, b) .0020, c) decide

2. b) 1/6, 5/6 c) 2/9, 1/9	17. a) .00098, b) no; other possibilities

3. c	18. a) .26, b) .3793, c) .4583, d) .16

4. a) 1/8, b) 1/8, c) ¾, d) ¾	19. .32

5. a) .9444, b) .8333, c) .7778, d) .9167, e) .9722	20. not independent events

6. 0.0015	21. .1472

7. 0.9437	22. .9999, almost 1, debatable

8. 0.5694	23. a) .5264, b) .4736, c) .4054, d) 529/770

9. 0.6914	e) not independent, f) 529/1626, g) same

10. 0.1	24. .5439

11. a) .7692, b) .0192, c) .3077, d) 3/52,	25. a) .8378, b) .0516, c) .0294, d) .0351

e) .0534 with, .0498 without	26. 6.2045 X 1023

12. a) .8, b) .3, c) .3, d) .2, e) .2	27. 1,663,200

13. a) 24/28, b) 16/28, c) 1, d) 4/28	28. 60,480 if 9 audition; 720 if 6 audition

14. a) .4, b) .14, c) .49, d) .5	29. 56

e) .86, f) .88, g) .18, h) .97	30. 120

15. a) .15, b) .2	31. a) 84, b) 504