Today is Thursday, October 10 Homework Notification · 2019. 10. 10. · Today is Thursday, October 10th Homework Notification No assignments are due today and no new assignments

Today is Thursday, October 10th

Homework Notification No assignments are due today and no new

assignments were given.

Hwk 3.1 Basic Probability Worksheet is due

tomorrow and was assigned on Wednesday

Group Quiz Tomorrow Basic Probability & Expected Value

Death Packet is Attached: Due Wednesday, October 23rd along with the Great Debate

Highly

FRQ Packet is Attached: Due Friday October 25th along with Presentations

Highly Recommended:

You can begin working on Death Packet problems 1-23

From the previous unit, you can work problems 44-50

Name:_______________________ Hwk 3.1 Basic Probability Work Sheet Period:______

Due: Friday, October 11th

1. A die is rolled, find the probability that an even number is obtained.

2. Two coins are tossed, find the probability that two heads are obtained.

3. Which of these numbers cannot be a probability? Justify your response.

a) -0.00001

b) 0.5

c) 1.001

d) 0

e) 1

f) 20%

4. Two dice are rolled, find the probability that the sum is

a) equal to 1

b) equal to 4

c) Equal to 5 or 6

d) less than 13

5. A die is rolled and a coin is tossed, find the probability that the die shows an odd number and the

coin shows a head.

6. A die is rolled what is the probability that the first 4 occurs on the 7th roll?

7. What is the probability that I roll three sixes in a row?

8. A card is drawn at random from a deck of cards. Find the probability of getting the 3 of diamonds.

9. A card is drawn at random from a deck of cards. Find the probability of getting a queen.

10. If 37% of high school students said that they exercise regularly, find the probability that 5 randomly

selected high school students all say that the exercise regularly. None are lying 11. If 25% of U.S. federal prison inmates are not U.S. citizens, find the probability that 2 randomly selected inmates will not be U.S. citizens.

12. A water pump contains three components, A, B, and C. The probabilities of failure for each

component in any one year are 0.02, 0.04, and 0.07, respectively. If any one component fails, the

pump will fail. If the components fail independently of one another, what is the probability that the

pump will fail in one year?




pump will not fail in one year?

14. If 2 cards are selected from a standard deck of cards. The first card is placed back in the deck before the second card is drawn. Find the following probabilities:

a) P(Heart and club) d) P(2 Aces)

b) P( Red card and 4 of spades) e) P(Queen of hearts and King of hearts)

c) P(Spade and Ace of hearts) f) P(2 of the same card) 15. Find the same probabilities for problem #12 but this time, the card is not placed back in the deck

before the 2nd card is drawn. 16. A bag contains 8 white marbles, 4 green marbles and 3 blue marbles. 2 marbles are selected at

random without replacement, find the following probabilities: a) P(both are green)

b) P(blue marble and white marble)

c) P(white marble and green marble)

d) P(At least one is red)

17. The medal distribution from 2000 Summer Olympic Games is shown on the table.

COUNTRY GOLD SILVER BRONZE Total

United States 39 25 33

Russia 32 28 28

China 28 16 15

Australia 16 25 17

Total Find these probabilities: a) What is the probability that a randomly chosen medal winner was from the U.S b) What is the probability that the medalist won gold c) What is the probability that the medalist won gold and was from the US d) Find the probability that the winner was from the US, given that she or he won a gold medal.

e) What is the probability that a medalist who won bronze was not from the U.S.

Name:_______________________ Basic Probability Work Sheet Period:______

1. A die is rolled, find the probability that an even number is obtained.

1,2,3,4,5,6 𝟑

𝟔 =

𝟏

𝟐 = .5

2. Two coins are tossed, find the probability that two heads are obtained. 𝟏

𝟐 ×

𝟏

𝟐 =

𝟏

𝟒

3. Which of these numbers cannot be a probability? Justify your response.

a) -0.00001 Probabilities can’t be negative

b) 0.5

c) 1.001 Probabilities can’t be greater than one

d) 0

e) 1

f) 20%

4. Two dice are rolled, find the probability that the sum is

a) equal to 1

0

b) equal to 4 𝟑

𝟑𝟔 =

𝟏

𝟏𝟐

e) Equal to 5 or 6 𝟒

𝟑𝟔 +

𝟓

𝟑𝟔 =

𝟗

𝟑𝟔 =

𝟏

𝟒

f) less than 13

1

5. A die is rolled and a coin is tossed, find the probability that the die shows an odd number and the

coin shows a head.

1, 2, 3, 5, 6 H, T 𝟑

𝟔 ×

𝟏

𝟐 =

𝟑

𝟏𝟐 =

𝟏

𝟒

6. A die is rolled what is the probability that the first 4 occurs on the 7th roll? 𝟓

𝟔 ×

𝟓

𝟔 ×

𝟓

𝟔 ×

𝟓

𝟔 ×

𝟓

𝟔 ×

𝟓

𝟔 ×

𝟏

𝟔 = .0558

7. What is the probability that I roll three sixes in a row. 𝟏

𝟔 ×

𝟏

𝟔 ×

𝟏

𝟔 =

𝟏

𝟐𝟓𝟔

8. A card is drawn at random from a deck of cards. Find the probability of getting the 3 of diamonds. 𝟏

𝟓𝟐

9. A card is drawn at random from a deck of cards. Find the probability of getting a queen. 𝟒

𝟓𝟐 =

𝟏

𝟏𝟑

10. If 37% of high school students said that they exercise regularly, find the probability that 5 randomly selected high school students all say that the exercise regularly. None are lying

(.37) (.37) (.37) (.37) (.37) = .00693

11. If 25% of U.S. federal prison inmates are not U.S. citizens, find the probability that 2 randomly selected inmates will not be U.S. citizens.

(.25) (.25) = .0625




pump will fail in one year?

1-[(1-.02) (1-.04) (1-.07)] = .125056

(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)




pump will not fail in one year?

[(1-.02) (1-.04) (1-.07)] = .874944

14. If 2 cards are selected from a standard deck of cards. The first card is placed back in the deck before the second card is drawn. Find the following probabilities:

a) P(Heart and club) 𝟏𝟑

𝟓𝟐 ×

𝟏𝟑

𝟓𝟐

b) P( Red card and 4 of spades) 𝟐𝟔

𝟓𝟐 ×

𝟏

𝟓𝟐

c) P(Spade and Ace of hearts) 𝟏𝟑

𝟓𝟐 ×

𝟏

𝟓𝟐

d) P(2 Aces) 𝟒

𝟓𝟐 ×

𝟒

𝟓𝟐 or

𝟏

𝟏𝟑 ×

𝟏

𝟏𝟑

e) P(Queen of hearts and King of hearts) 𝟏

𝟓𝟐 ×

𝟏

𝟓𝟐

f) P(2 of the same card) 𝟏

𝟓𝟐

15. Find the same probabilities for problem #14 but this time, the card is not placed back in the deck before the 2nd card is drawn.

a) 𝟏𝟑

𝟓𝟐 ×

𝟏𝟑

𝟓𝟏

b) 𝟐𝟔

𝟓𝟐 ×

𝟏

𝟓𝟏

c) 𝟏𝟑

𝟓𝟐 ×

𝟏

𝟓𝟏

d) 𝟒

𝟓𝟐 ×

𝟑

𝟓𝟏

e) 𝟏

𝟓𝟐 ×

𝟏

𝟓𝟏

f) 0

16. A bag contains 8 white marbles, 4 green marbles and 3 blue marbles. 2 marbles are selected at random without replacement, find the following probabilities:

a. P(both are green) 𝟒

𝟏𝟓 ×

𝟑

𝟏𝟒

b. P(blue marble and white marble) 𝟑

𝟏𝟓 ×

𝟖

𝟏𝟒

c. P(white marble and green marble) 𝟖

𝟏𝟓 ×

𝟒

𝟏𝟒

d. P(At least one is red) (0)

17. The medal distribution from 2000 Summer Olympic Games is shown on the table.

COUNTRY GOLD SILVER BRONZE Total

United States 39 25 33 97

Russia 32 28 28 88

China 28 16 15 59

Australia 16 25 17 58

Total 115 94 93 302 Find these probabilities:

a. What is the probability that a randomly chosen medal winner was from the U.S 𝟗𝟕

𝟑𝟎𝟐

b. What is the probability that a medalist won gold 𝟏𝟏𝟓

𝟑𝟎𝟐

c. What is the probability that the medalist won gold and was from the US 𝟑𝟗

𝟑𝟎𝟐

d. Find the probability that the winner was from the US, given that she or he won a gold medal. 𝟑𝟗

𝟏𝟏𝟓

e. What is the probability that a medalist who won bronze was not from the U.S. 𝟐𝟖+𝟏𝟓+𝟏𝟕

𝟗𝟑

Name:__________________________ Due Wednesday, October 23rd Period:______

Death Packet: Basic, Classical & Conditional Probability

1. It is estimated that 30% of all cars parked in a metered lot outside City Hall receive tickets for

meter violations. In a random sample of 5 cars parked in this lot, what is the probability that at

least one receives a parking ticket?

(A) 1 - (.3)5

(B) 1 - (.7)5

(C) 5(.3)(.7)4

(D) 5(.3)4(.7)

(E) 5(.3)4(.7) + 10(.3)3(.7)2 + 10(.3)2(.7)3 + 5(.3)(.7)4 + (.7)5

2. Suppose that 54% of the graduates from your high school go on to 4-year colleges, 20% go on to 2-

year colleges, 19% find employment, and the remaining 7% search for a job. If a randomly selected

student is not going on to a 2-year college, what is the probability she will be going on to a 4-year

college?

(A) .460

(B) .540

(C) .630

(D) .675

(E) .730

3. Suppose you toss a fair die three times and it comes up an even number each time. Which of the

following is a true statement?

(A) By the law of large numbers, the next toss is more likely to be an odd number than another even

number.

(B) Based on the properties of conditional probability the next toss is more likely to be an even

number given that three in a row have been even.

(C) Dice actually do have memories, and thus the number that comes up on the next toss will be

influenced by the previous tosses.

(D) The law of large numbers tells how many tosses will be necessary before the percentages of

evens and odds are again in balance.

(E) The probability that the next toss will again be even is .5.

4. There are two games involving flipping a coin. In the first game you win a prize if you can throw

between 45% and 55% heads. In the second game you win if you can throw more than 80% heads.

For each game would you rather flip coin 30 times or 300 times?

(A) 30 times for each game

(B) 300 times for each game

(C) 30 times for the first game and 300 times for the second

(D) 300 times for the first game and 30 times for the second

(E) The outcomes of the games do not depend on the number flips.

5. There are five outcomes to an experiment and a student calculates the respective probabilities of

the outcomes to be .34, .50, 0, and -.26. The proper conclusion is that

(A) The sum of the individual probabilities is 1.

(B) One of the outcomes will never occur.

(C) One of the outcomes will occur 50 percent of the time.

(D) All of the above are true.

(E) The student made an error.

6. There are two games involving flipping a fair coin. In the first game, you win a prize if you can

throw between 45 percent and 55 percent heads; in the second game, you win if you can throw more

than 60 percent heads. For each game, would rather flip the coin 30 times or 300 times?



(C) 30 times for the first game, and 300 for the second

(D) 300 times for the first game, and 30 for the second

(E) The outcomes of the games do not depend on the number of flips.

7. Which of the following is not a probability density function?

(A) f(x) = 1, 0 ≤ x ≤ 1

(B) f(x) = 0.2, 0 ≤ x ≤ 5

(D) f(x) = 2x, 0 ≤ x ≤ 1

(E) f(x) = 3x, 0 ≤ x ≤ 3

8. Suppose you toss a fair coin ten times and it comes up heads every time. Which of the following is a

true statement?

(A) By the Law of Large Numbers, the next toss is more likely to be tails than another heads.

(B) By the properties of conditional probability, the next toss is more likely to be heads given that

then tosses in arrow have been heads.

(C) Coins actually do have memories, and thus what comes up on the next toss is influenced by the

past tosses.

(D) The Law of Large Numbers tells how many tosses will be necessary before the percentage of

heads and tails are again in balance.

(E) None of the above are true statements.

9. According to one poll, only 8 percent of the public say they “trust Congress.” In a simple random

sample of ten people, what is the probability that at least one person “trusts Congress”?

(A) .188

(B) .378

(C) .434

(D) .566

(E) .622

(C) f(x) = 0.1, 0 ≤ x ≤ 4

0.2, 4 < x ≤ 7

10. A mortgage company advertises that 85 percent of applications are approved. In a random sample

of 30 applications, what is the expected number that will be turned down?

(A) 30(.85)

(B) 30(.15)

(C) 30(.85(.15)

(D) √30(. 85)(.15)

(E) √(.85)(.15)

30

11. It is estimated that 20 percent of all drivers do not signal when changing lanes. In a random sample

of four drivers, what is the probability that at least one doesn’t signal when changing lanes?

(A) 1 – (.2)4

(B) 1 - (.8)4

(C) 4(.2)(.8)3

(D) 4(.2)3(.8)

(E) 4(.2)3(.8) + 4(.2)2(.8)2 + 4(.2)(.8)3 + (.8)4

12. Three-fourths of college students change their major at least once. The reasons for changing and

what they change to are as follows:

Reason Change in career

interests

Advisor

Suggestion

Professor

Suggestion

Other

Reason

Probability .55 .1 .20 .15

Reason Related field Liberal Arts Pre-

professional

Probability .55 .1 .20

Assuming reasons and what students change to are independent, what is the probability that a

college student decides to change a major, based on advisor suggestion, to pre-professional?

(A) 0.015

(B) .0200

(C) .0263

(D) .0350

(E) .0467

13. There are 8,253 men and 10,327 women at a state university. If 43 percent of the men and 27

percent of the women are business majors, what is the expected number of business majors in a

random sample of 200 students?

(A) 31.7

(B) 34.1

(C) 63.4

(D) 68.2

(E) 70.0

14. A company bids on three independent contracts with probabilities of winning the contracts .1, .25,

and .3 respectively. What is the probability of winning at least one contract?

(A) .35

(B) .4725

(C) .5275

(D) .65

(E) .9925

15. Which of the following is not a valid discrete probability distribution for the set {x1, x2, x3}?

(A) P(x1) = 1, P(x2) = 0, P(x3) = 0

(B) P(x1) = 1

3, P(x2) =

1

3, P(x3) =

1

3

(C) P(x1) = 1

2, P(x2) =

1

3, P(x3) =

1

6

(D) P(x1) = 2

3, P(x2) =

2

3, P(x3) = −

1

3

(E) All the above are valid probability distributions.

16. Suppose a manufacturer knows that 20 percent of the circuit boards coming off the assembly line

have a minor defect. If an inspector keeps inspecting boards until he comes upon one with the

defect, what is the probability he will have to inspect at most three boards?

(A) .128

(B) .384

(C) .488

(D) .512

(E) .896

17. A magazine has 1,620,000 subscribers, of whom 640,000 are women and 980,000 are men. Thirty

percent of the women read the advertisements in the magazine and 50 percent of the men read the

advertisements in the magazine. A random sample of 100 subscribers is selected. What is the

expected number of subscribers in the sample who read the advertisements?

(A) 30

(B) 40

(C) 42

(D) 50

(E) 80

18. Five managers and five employees are on a grievance committee. A three-person subcommittee is

formed by a random selection from the ten committee members. What is the probability that all

three members of the subcommittee are managers?

(A) 1

12

(B) 1

16

(C) 3

16

(D) 5

16

(E) 1

2

19. Is there a home field advantage in professional baseball games? Emotional support from the fans

and familiarity with the field seem to make a difference as the home team has won in approximately

5/9 of World Series games. Assuming this probability is constant and games are independent, if the

home team wins the first game, what is the probability that the home team also wins the next two

home games?

(A) (5/9)2

(B) (5/9)3

(C) 3(5/9)2(4/9)

(D) 1 - (5/9)3

(E) 1 - (4/9)2

20. There are two games involving flipping a fair coin. In the first game, you win a prize if you can

throw between 45 percent and 55 percent heads. In the second game, you win if you can throw more

than 60 percent heads. For each game, would your rather flip the coin 20 times or 40 times?



(C) 20 times for the first game and 40 times for the second

(D) 40 times for the first game and 20 times for the second

(E) The outcomes of the games do not depend on the number of flips.

21. Joe and Matthew plan to visit a bookstore. Based on their previous visits to this bookstore, the

probability distributions of the number of books they will buy are given below.

Number of books

Joe will buy 0 1 2

Probability 0.50 0.25 0.25

Number of books

Matthew will buy 0 1 2


Assuming that Joe and Matthew make their decisions independently, what is the probability that

they will purchase no books on this visit to the bookstore?

(A) 0.0625

(B) 0.1250

(C) 0.1875

(D) 0.2500

(E) 0.7500

22. A chess master wins 80% of her games, loses 5%, and draws the rest. If she receives 1 point for a

win, ½ point for a draw, and no point for a loss, what is true about the sampling distribution X of the

points scored in two independent games?

(A) X takes on the values 0, 1, and 2 with respective probabilities 0.10, 0.26 and 0.64.

(B) X takes on the values 0, ½, 1, 1½, and 2 with respective probabilities 0.0025, 0.015, 0.1025, 0.24,

and 0.64.

(C) X takes on values according to a binomial distribution with n = 2 and p = 0.8.

(D) X takes on values according to a binomial distribution with mean 1(.8) + ½(.15) + 0(.05).

(E) X takes on values according to a distribution with mean (2)(.8) and standard deviation √𝟐(. 𝟖)(. 𝟐).

23. A banking corporation advertises that 90% of the loan applications it receives are approved within 24

hours. In a random sample of 50 applications, what is the expected number of loan applications that

will be turned down?

(A) 50(.90)

(B) 50(.10)

(C) 50(.90)(.10)

(D) √𝟓𝟎(. 𝟗𝟎)(. 𝟏𝟎)

(E) √(.𝟗𝟎)(.𝟏𝟎)

𝟓𝟎

24. Given the probabilities P(A) = .3 and P(B) = .2 what is the probability of the union P(A∪B) if A and B

are mutually exclusive? If A and B are independent? If B is a subset of A?

(A) .44, 0.5, 0.2

(B) .44, 0.5, 0.3

(C) 0.5, .44, 0.2

(D) 0.5, .44, 0.3

(E) 0.0, 0.5 0.3

25. Given that P(E) = .32, P(F) = .15, and P(E∩F) = .048, which of the following is a correct conclusion?

(A) The events E and F are both independent and mutually exclusive.

(B) The events E and F are neither independent nor mutually exclusive.

(C) The events E and F are mutually exclusive but not independent.

(D) The events E and F are independent but not mutually exclusive.

(E) The events E and F are independent, but there is insufficient information to determine whether

or not they are mutually exclusive.

26. Suppose that the probabilities that an answer can be found on Google is .95, on Answers.com is .92,

and on both websites is .874. Are the possibilities of finding the answers on the two websites

independent?

(A) Yes, because (.95)(.92) = .874

(B) No, because (.95)(.92) = .874

(C) Yes, because .95 > .92 >.874

(D) No, because .5(.95 + .92) ≠ .874

(E) There is insufficient information to answer this question.

27. If P(A) = .25 and P(B) =.34, what is the P(A∪B) if A and B are independent?

(A) .085

(B) .505

(C) .590

(D) .675


28. Given that 49.0 percent of the U.S. population are male, and 12.1 percent of the population are over

65 years in age, can we conclude that 5.93% of the population are male and over the age of 65?

(A) Yes, by the multiplication rule

(B) Yes, by the conditional probabilities

(C) Yes, by the law of large numbers

(D) No, because the events are not independent

(E) No, because the events are not mutually exclusive

29. Given the probabilities P(A) = .3 and P(A∪B) = .7, what is the probability P(B) if A and B are mutually

exclusive? If A and B are independent?

(A) .4, .3

(B) .4, 𝟒

𝟕

(C) 𝟒

𝟕, .4

(D) .7, 𝟒

𝟕

(E) .7, .3

30. An experiment has three mutually exclusive outcomes, A, B, and C. If P(A) = 0.12, P(B) = 0.61, and

P(C) = 0.27, which of the following must be true?

I. A and C are independent.

II. P(A and B) = 0

III. P(B or C) = P(B) + P(C)

(A) I only

(B) I and II only

(C) I and III only

(D) II and III only

(E) I, II, and III

31. Given two events, E and F, such that P(E) = .340, P(F) = .450, and P(E∪F) = .637, then the two events

are:

(A) Independent and mutually exclusive.

(B) Independent, but not mutually exclusive.

(C) Mutually exclusive, but not independent.

(D) Neither independent nor mutually exclusive.

(E) There is not enough information to answer this question.

32. Following are parts of the probability distribution for the random variables X and Y.

X P(X) Y P(Y)

1 ? 1 .4

2 .2 2 ?

3 .3 3 .3

4 ?

If X and Y are independent and the joint probability P(X=1, Y=2) = .12 what is P(X=4)?

(A) .1

(B) .2

(C) .3

(D) .4

(E) .5

33. Suppose P(X) = .35 and P(Y) = .40. If P(X|Y) = .28, what is P(Y|X)?

(A) (.𝟐𝟖)(.𝟑𝟓)

.𝟒𝟎

(B) (.𝟐𝟖)(.𝟒𝟎)

.𝟑𝟓

(C) (.𝟑𝟓)(.𝟒𝟎)

.𝟐𝟖

(D) .𝟐𝟖

.𝟒𝟎

(E) .𝟐𝟖

.𝟑𝟓

34. A plumbing contractor obtains 60% of her boiler circulators from a company whose defect rate is

0.005, and the rest from a company whose defect rate is 0.010. If a circulator is defective, what is

the probability that it came from the first company?

(A) .429

(B) .500

(C) .571

(D) .600

(E) .750

35. Given a probability of 0.65 that interest rates will jump this year, and a probability of 0.72 that if

interest rates jump the stock market will decline, what is the probability that interest rates will

jump and the stock market will decline?

(A) .72 + .65 – (.72)(.65)

(B) (.72)(.65)

(C) 1 – (.72)(.65)

(D) .𝟔𝟓

.𝟕𝟐

(E) 1 - .𝟔𝟓

.𝟕𝟐

36. The following is from a particular region’s mortality table.

Age 0 20 40 60 80

Number Surviving 10,000 9,700 9,240 7,800 4,300

What is the probability that a 20-year-old will survive to be 60?

(A) .9700

(B) .8041

(C) .7800

(D) .4419

(E) .1959

37. A computer manufacturer sets up three locations to provide technical support for its customers.

Logs are kept noting whether or not calls about problems are solved successfully. Data from a

sample of 1,000 calls are summarized in the following table:

Assuming there is no association between location and whether or not a problem is resolved

successfully, what is the expected number of successful calls (problem solved) from location 1?

(A) (𝟑𝟐𝟓)(𝟒𝟓𝟎)

𝟕𝟎𝟎

(B) (𝟑𝟐𝟓)(𝟕𝟎𝟎)

𝟒𝟓𝟎

(C) (𝟑𝟐𝟓)(𝟒𝟓𝟎)

𝟏𝟎𝟎𝟎

(D) (𝟑𝟐𝟓)(𝟕𝟎𝟎)

𝟏𝟎𝟎𝟎

(E) (𝟒𝟓𝟎)(𝟕𝟎𝟎)

𝟏𝟎𝟎𝟎

38. The probability that a person will show a certain gene-transmitted trait is 0.8 if the father shows

the trait and 0.06 if the father doesn’t show the trait. Suppose that the children in a certain

community come from families in 25% of which the father shows the trait. Given that a child shows

the trait, what is the probability that her father shows the trait?

(A) .245

(B) .250

(C) .750

(D) .816

(E) .860

Location

1 2 3 Total

Problem solved 325 225 150 700

Problem not solved 125 100 75 300

Total 450 325 225 1000

39. Suppose 4% of the population have a certain disease. A laboratory blood test gives a positive reading

for 95% of people who have the disease and for 5% of people who do not have the disease. If a

person tests positive, what is the probability the person has the disease?

(A) .038

(B) .086

(C) .442

(D) .558

(E) .950

40. The Air Force received 40 percent of its parachutes from company C1 and the rest from company C2.

The probability that a parachute will fail to open is .0025 or .002, depending on whether it is from

company C1 or C2 respectively. If a randomly chosen parachute fails to open, what is the probability

that it is from company C1?

(A) .0010

(B) .0022

(C) .4025

(D) .4545

(E) .5455

41. Suppose that 62 percent of the graduates from your high school go on to four-year colleges, 15

percent go on to two-year colleges, 18 percent find employment, and the remaining graduates search

for a job. If a randomly selected student is not going on to a four-year college, what is the

probability he or she will find employment?

(A) .440

(B) .474

(C) .526

(D) .545

(E) .560

42. Suppose P(X) = .25 and P(Y) = .40. If P(X l Y) = .20, what is P(Y l X)?

(A) .10

(B) .125

(C) .32

(D) .45

(E) .50

43. Suppose that for a certain coastal city, in any given year the probability of a major hurricane hitting

is .4, the probability of flooding is .3, and the probability of major hurricane and flooding is .2. What

is the probability of flooding given that a major hurricane hits?

(A) .200

(B) .286

(C) .500

(D) .667

(E) .750

44. Suppose X and Y are random variables with μx = 32, σx = 5, μy = 44, σy = 12. Given that X and Y are

independent, what are the mean and standard deviation of the random X + Y?

(A) μx+y = 76, σx+y = 8.5

(B) μx+y = 76, σx+y = 13

(C) μx+y = 76, σx+y = 17

(D) μx+y = 38, σx+y = 17


45. The appraised values of houses in a city have a mean of $125,000 with a standard deviation of

$23,000. Because of a new teachers’ contract, the school district needs an extra 10% in funds

compared to the previous year. To raise this additional money, the city instructs the assessment

office to raise all appraised house values by $5,000. What will be the new standard deviation of the

appraised values of houses in the city?

(A) $23,000

(B) $25,000

(C) $28,000

(D) $30,300

(E) $30,800

46. Suppose X and Y are independent random variables with E(X) = 37, var(X) = 5, E(Y) = 62, and var(Y) =

12. What are the expected value and variance of the random variable of X + Y?

(A) E(X + Y) = 99, var(X + Y) = 8.5

(B) E(X + Y) = 99, var(X + Y) = 13

(C) E(X + Y) = 99, var(X + Y) = 17

(D) E(X + Y) = 49.5, var(X + Y) = 17


47. Motor vehicle death rates per 100,000 people among the 50 states have a mean of 13.1 with a

standard deviation of 4.9, while firearm death rates per 100,000 people among the 50 states have a

mean of 12.0 with a standard deviation of 3.7. What would be the firearm death rate that has the

same z-score as a motor vehicle death rate of 15.0 per 100,000?

(A) 13.4

(B) 13.5

(C) 13.9

(D) 14.5

(E) 17.1

48. Suppose X and Y are random variables with μx = 32, σx = 5, μy = 44, σy = 12. Given that X and Y are

independent, what are the mean and standard deviation of the random X + Y?

(A) μx+y = 76, σx+y = 8.5

(B) μx+y = 76, σx+y = 13

(C) μx+y = 76, σx+y = 17

(D) μx+y = 38, σx+y = 17


49. The financial aid office at a state university conducts a study to determine the total student costs

per semester. All students are charged $4,500 for tuition. The mean cost for books is $350 with a

standard deviation f $65. The mean outlay for room and board is $2,800 with a standard deviation

of $380. The mean personal expenditure is $675 with a standard deviation of $125. Assuming

independence among categories, what is the standard deviation of the total student costs?

(A) $24

(B) $91

(C) $190

(D) $405

(E) $570

50. A television game show has three payoffs with the following probabilities:

Payoff ($) 0 500 5,000

Probability .7 .25 .05

What are the mean and standard deviation of the payoff variable?

(A) 𝜇 = 375, 𝜎 = 361

(B) 𝜇 = 375, 𝜎 = 1,083

(C) 𝜇 = 1,833, 𝜎 = 1,816

(D) 𝜇 = 1,833, 𝜎 = 2,248

(E) None of the above gives a set of correct answers.

Name:_______________________Due Friday October 25th with Presentations Period______

FRQ Test Review: Basic, Classical and Conditional Probability

Directions: Show all your work on a Separate sheet of Paper. Turn in the Answers and your work,

1. 2014 Question 1 An administrator at a large university is interested in determining whether

the residential status of a student is associated with level of participation in extracurricular activities.

Residential status is categorized as on campus for students living in university housing and off campus

otherwise. A simple random sample of 100 students in the university was taken, and each student was

asked the following two questions.

Are you an on campus student or an off campus student?

In how many extracurricular activities do you participate?

The responses of the 100 students are summarized in the frequency table shown.

Residential Status

Level of Participants in

Extracurricular Activities

On Campus Off Campus Total

No Activities 9 30 39

One Activity 17 25 42

Two or more activities 7 12 19

Total 33 67 100

(a) Calculate the proportion of on campus students in the sample who participate in at least one

extracurricular activity and the proportion of off campus students in the sample who participate

in at least one extracurricular activity.

On campus proportion: 24/33=.72

Off campus proportion: 37/67=.55

The responses of the 100 students are summarized in the segmented bar graph shown.

(b) Write a few sentences summarizing what the graph reveals about the association between residential

status and level of participation in extracurricular activities among the 100 students in the sample.

2. 1997 Problem 3 A laboratory test for the detection of a certain disease gives a positive result 5

percent of the time for people who do not have the disease. The test gives a negative result 0.3 percent

of the time for people who have the disease. Large-scale studies have shown that the disease occurs in

about 2 percent of the population.

(a) What is the probability that a person selected at random would test positive for this

disease? Show your work.

(b) What is the probability that a person selected at random who tests positive for the disease does

not have the disease? Show your work

3. 2010 Form B Question 5 An advertising agency in a large city is conducting a survey of adults to

investigate whether there is an association between highest level of education achievement and

primary source for news. The company takes a random sample of 2,500 adults in the city. The results

are shown in the table below. Highest Level of Educational Achievement

Primary Source

for News

Not High School

Graduate

High School Graduate but

not College Graduate

College

Graduate Total

Newspapers 49 205 188 442

Local television 90 170 75 335

Cable television 113 496 147 756

Internet 41 401 245 687

None 77 165 38 280

Total 370 1,437 693 2,500

a) If an adult is to be selected at random from this sample, what is the probability that the selected

adult is a college graduate or obtains news primarily from the internet?

b) If an adult who is a college graduate is to be selected at random from this sample, what is the

probability that the selected adult obtains news primarily from the internet?

c) When selecting an adult at random from the sample of 2,500 adults, are the events “is a college

graduate” and “obtains news primarily from the internet” independent? Justify your answer.

4. 2009B Question 2 The ELISA tests whether a patient has contracted HIV. The ELISA is said to

be positive if it indicates that HIV is present in a blood sample, and the ELISA is said to be

negative if it does not indicate that HIV is present in a blood sample. Instead of directly measuring

the presence of HIV, the ELISA measures levels of antibodies in the blood that should be elevated

if HIV is present. Because of variability in antibody levels among human patients, the ELISA does

not always indicate the correct result.

As part of a training program, staff at a testing lab applied the ELISA to 500 blood samples known

to contain HIV. The ELISA was positive for 489 of those blood samples and negative for the other 11

samples. As part of the same training program, the staff also applied the ELISA to 500 other blood

samples known to not contain HIV. The ELISA was positive for 37 of those blood samples and

negative for the other 463 samples.

(a) When a new blood sample arrives at the lab, it will be tested to determine whether HIV is

present. Using the data from the training program, estimate the probability that the ELISA

would be positive when it is applied to a blood sample that does not contain HIV.

(b) Among the blood samples examined in the training program that provided positive ELISA results

for HIV, what proportion actually contained HIV?

(c) When a blood sample yields a positive ELISA result, two more ELISAs are performed on the same

blood sample. If at least one of the two additional ELISAs is positive, the blood sample is

subjected to a more expensive and more accurate test to make a definitive determination of

whether HIV is present in the sample. Repeated ELISAs on the same sample are generally

assumed to be independent. Under the assumption of independence, what is the probability that a

new blood sample that comes into the lab will be subjected to the more expensive test if that

sample does not contain HIV?

5. 1999 Problem 5 Die A has four 9’s and two 0’s on its faces. Die B has four 3’s and two 11’s on its

faces. When either of these dice is rolled, each face has an equal chance of landing on top. Two

players are going to play a game. The first player selects a die and rolls it. The second player rolls

the remaining die. The winner is the player whose die has the higher number on top.

(a) Suppose you are the first player and you want to win the game. Which die would you select?

Justify your answer.

(b) Suppose the player using die A receives 45 tokens each time he or she wins the game. How many

tokens must the player using die B receive each time he or she wins in order for this to be a fair

game? Explain how you found your answer.

6. 2008 Problem 3 A local arcade is hosting a tournament in which contestants play an arcade game

with possible scores ranging from 0 to 20. The arcade has set up multiple game tables so that all

contestants can play the game at the same time; thus contestant scores are independent. Each

contestant’s score will be recorded as he or she finishes, and the contestant with the highest score

is the winner.

After practicing the game many times, Josephine, one of the contestants, has established the

probability distribution of her scores, shown in the table below.

Josephine’s Distribution

Score 16 17 18 19

Probability 0.10 0.30 0.40 0.20

Crystal, another contestant, has also practiced many times. The probability distribution for her

scores is shown in the table below. Crystal’s Distribution

Score 17 18 19


(a) Calculate the expected score for each player.

(b) Suppose that Josephine scores 16 and Crystal scores 17. The difference (Josephine minus Crystal)

of their scores is –1. List all combinations of possible scores for Josephine and Crystal that will

produce a difference (Josephine minus Crystal) of –1, and calculate the probability of each

combination.

(c) Find the probability that the difference (Josephine minus Crystal) in their scores is –1.

(d) The table below lists all the possible differences in the scores between Josephine and Crystal and

some associated probabilities. Distribution (Josephine minus Crystal)

Difference -3 -2 -1 0 1 2

Probability 0.015 0.325 0.260 0.090

Complete the table and calculate the probability that Crystal’s score will be higher than Josephine’s

score.

7. 2015 Question 3. A shopping mall has three automated teller machines (ATMs). Because the

machines receive heavy use, they sometimes stop working and need to be repaired. Let the random

variable X represent the number of ATMs that are working when the mall opens on a randomly

selected day. The table shows the probability distribution of X.

Number of ATMs working when the mall opens 0 1 2 3

0.15 0.21 0.40 0.24

(a) What is the probability that at least one ATM is working when the mall opens?

(b) What is the expected value of the number of ATMs that are working when the mall opens?

(c) What is the probability that all three ATMs are working when the mall opens, given that at least

one ATM is working?

(d) Given that at least one ATM is working when the mall opens, would the expected value of the

number of ATMs that are working be less than, equal to, or greater than the expected value from

part (b) ? Explain.

8. 2011 Problem 2 The table below shows the political party registration by gender of all 500

registered voters in Franklin Township.

PARTY REGISTRATION – FRANKLIN TOWNSHIP

Party W Party X Party Y Total

Female 60 120 120 300

Male 28 124 48 200

Total 88 244 168 500

(a) Given that a randomly selected registered voter is a male, what is the probability that he is registered

for Party Y? 𝐶𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙

𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙=

𝑃𝑎𝑟𝑡𝑦 𝑌

𝑀𝑎𝑙𝑒=

48

200=

6

25 = .24

(b) Among the registered voters of Franklin Township, are the events “is a male” and “is registered for

Party Y” independent? Justify your answer based on probabilities calculated from the table above. and .

Documents

Today is Thursday, October 10 Homework Notification · 2019. 10. 10. · Today is Thursday, October 10th Homework Notification No assignments are due today and no new assignments