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Page 1: Probability: Homework - OpenStax CNX · 2018-05-21 · Probability: Homework * ... solve problems involving conditional probability; ... Three marbles are drawn from a jar containing

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Probability: Homework*

UniqU, LLC

Based on Applied Finite Mathematics: Chapter 07� by

Rupinder Sekhon

This work is produced by OpenStax-CNX and licensed under the

Creative Commons Attribution License 3.0�

Abstract

This chapter covers principles of probability. After completing this chapter students should be able to:

write sample spaces; determine whether two events are mutually exclusive; use the addition rule; calculate

probabilities using tree diagrams and combinations; solve problems involving conditional probability;

determine whether two events are independent.

1 SAMPLE SPACES AND PROBABILITY

In problems 1 - 6, write a sample space for the given experiment.

Exercise 1 (Solution on p. 16.)

A die is rolled.

Exercise 2A penny and a nickel are tossed.

Exercise 3 (Solution on p. 16.)

A die is rolled, and a coin is tossed.

Exercise 4Three coins are tossed.

Exercise 5 (Solution on p. 16.)

Two dice are rolled.

Exercise 6A jar contains four marbles numbered 1, 2, 3, and 4. Two marbles are drawn.

In problems 7 - 12, a card is selected from a deck. Find the following probabilities.

Exercise 7 (Solution on p. 16.)

P (an ace) (1)

*Version 1.1: Jul 15, 2011 11:41 pm -0500�http://cnx.org/content/m18907/1.1/�http://creativecommons.org/licenses/by/3.0/

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Exercise 8

P (a red card) (2)

Exercise 9 (Solution on p. 16.)

P (a club) (3)

Exercise 10

P (a face card) (4)

Exercise 11 (Solution on p. 16.)

P (a jack or spade) (5)

Exercise 12

P (a jack and a spade) (6)

A jar contains 6 red, 7 white, and 7 blue marbles. If a marble is chosen at random, �nd the followingprobabilities.

Exercise 13 (Solution on p. 16.)

P (red) (7)

Exercise 14

P (white) (8)

Exercise 15 (Solution on p. 16.)

P (red or blue) (9)

Exercise 16

P (red and blue) (10)

Consider a family of three children. Find the following probabilities.

Exercise 17 (Solution on p. 16.)

P (two boys and a girl) (11)

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Exercise 18

P (at least one boy) (12)

Exercise 19 (Solution on p. 16.)

P (children of both sexes) (13)

Exercise 20

P (at most one girl) (14)

Two dice are rolled. Find the following probabilities.

Exercise 21 (Solution on p. 16.)

P (the sum of the dice is 5) (15)

Exercise 22

P (the sum of the dice is 8) (16)

Exercise 23 (Solution on p. 17.)

P (the sum is 3 or 6) (17)

Exercise 24

P (the sum is more than 10) (18)

A jar contains four marbles numbered 1, 2, 3, and 4. If two marbles are drawn, �nd the following probabilities.

Exercise 25 (Solution on p. 17.)

P (the sum of the number is 5) (19)

Exercise 26

P (the sum of the numbers is odd) (20)

Exercise 27 (Solution on p. 17.)

P (the sum of the numbers is 9) (21)

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Exercise 28

P (one of the numbers is 3) (22)

2 MUTUALLY EXCLUSIVE EVENTS AND THE ADDITION RULE

Determine whether the following pair of events are mutually exclusive.

Exercise 29 (Solution on p. 17.)

A = {A person earns more than $25,000} (23)

B = {A person earns less than $20,000} (24)

Exercise 30A card is drawn from a deck.

C = {It is a King}D = {It is a heart}. (25)

Exercise 31 (Solution on p. 17.)

A die is rolled.

E = {An even number shows} (26)

F = {A number greater than 3 shows} (27)

Exercise 32Two dice are rolled.

G = {The sum of dice is 8} (28)

H = {One die shows a 6} (29)

Exercise 33 (Solution on p. 17.)

Three coins are tossed.

I = {Two heads come up} (30)

J = {At least one tail comes up} (31)

Exercise 34A family has three children.

K = {First born is a boy} (32)

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L = {The family has children of both sexes} (33)

Use the addition rule to �nd the following probabilities.

Exercise 35 (Solution on p. 17.)

A card is drawn from a deck, and the events C and D are as follows:

C = {It is a king} (34)

D = {It is a heart} (35)

Find P (C or D).

Exercise 36A die is rolled, and the events E and F are as follows:

E = {An even number shows} (36)

F = {A number greater than 3 shows} (37)

Find P (E or F ).

Exercise 37 (Solution on p. 17.)

Two dice are rolled, and the events G and H are as follows:

G = {The sum of dice is 8} (38)

H = {Exactly one die shows a 6} (39)

Find P (G or H).

Exercise 38Three coins are tossed, and the events I and J are as follows:

I = {Two heads come up} (40)

J = {At least one tail comes up} (41)

Find P (I or J).

Exercise 39 (Solution on p. 17.)

At De Anza college, 20% of the students take Finite Mathematics, 30% take Statistics and 10%take both. What percentage of the students take Finite Mathematics or Statistics?

Exercise 40This quarter, there is a 50% chance that Jason will pass Accounting, a 60% chance that he willpass English, and 80% chance that he will pass at least one of these two courses. What is theprobability that he will pass both Accounting and English?

The following table shows the distribution of Democratic and Republican U.S. Senators by gender.

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MALES(M) FEMALES(F) TOTAL

DEMOCRATS(D) 39 4 43

REPUBLICANS(R) 52 5 57

TOTALS 91 9 100

Table 1

Use this table to determine the following probabilities.

Exercise 41 (Solution on p. 17.)

P (M and D) (42)

Exercise 42

P (F and R) (43)

Exercise 43 (Solution on p. 17.)

P (M or D) (44)

Exercise 44

P(F or RC

)(45)

Exercise 45 (Solution on p. 17.)

P(MC or R

)(46)

Exercise 46

P (M or F ) (47)

Again, use the addition rule to determine the following probabilities.

Exercise 47 (Solution on p. 17.)

If P (E) = .5 and P (F ) = .4 and E and F are mutually exclusive, �nd P (E and F ).

Exercise 48If P (E) = .4 and P (F ) = .2 and E and F are mutually exclusive, �nd P (E or F ).

Exercise 49 (Solution on p. 17.)

If P (E) = .3 and P (E or F ) = .6 and P (E and F ) = .2, �nd P (F ).

Exercise 50If P (E) = .4, P (F ) = .5 and P (E or F ) = .7, �nd P (E and F ).

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3 CALCULATING PROBABILITIES USING TREE DIAGRAMS AND COM-

BINATIONS

Two apples are chosen from a basket containing �ve red and three yellow apples. Draw a tree diagram below,and �nd the following probabilities.

Exercise 51 (Solution on p. 17.)

P (both red) (48)

Exercise 52

P (one red, one yellow) (49)

Exercise 53 (Solution on p. 17.)

P (both yellow) (50)

Exercise 54

P (First red and second yellow) (51)

A basket contains six red and four blue marbles. Three marbles are drawn at random. Find the followingprobabilities using the method shown in . Do not use combinations.

Exercise 55 (Solution on p. 17.)

P (All three red) (52)

Exercise 56

P (two red, one blue) (53)

Exercise 57 (Solution on p. 17.)

P (one red, two blue) (54)

Exercise 58

P (�rst red, second blue, third red) (55)

Three marbles are drawn from a jar containing �ve red, four white, and three blue marbles. Find thefollowing probabilities using combinations.

Exercise 59 (Solution on p. 18.)

P (all three red) (56)

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Exercise 60

P (two white and 1 blue) (57)

Exercise 61 (Solution on p. 18.)

P (none white) (58)

Exercise 62

P (at least one red) (59)

A committee of four is selected from a total of 4 freshmen, 5 sophomores, and 6 juniors. Find the probabilitiesfor the following events.

Exercise 63 (Solution on p. 18.)

At least three freshmen.

Exercise 64No sophomores.

Exercise 65 (Solution on p. 18.)

All four of the same class.

Exercise 66Not all four from the same class.

Exercise 67 (Solution on p. 18.)

Exactly three of the same class.

Exercise 68More juniors than freshmen and sophomores combined.

Five cards are drawn from a deck. Find the probabilities for the following events.

Exercise 69 (Solution on p. 18.)

Two hearts, two spades, and one club.

Exercise 70A �ush of any suit(all cards of a single suit).

Exercise 71 (Solution on p. 18.)

A full house of nines and tens(3 nines and 2 tens).

Exercise 72Any full house.

Exercise 73 (Solution on p. 18.)

A pair of nines and tens.

Exercise 74Two pairs

Do the following birthday problems.

Exercise 75 (Solution on p. 18.)

If there are �ve people in a room, what is the probability that no two have the same birthday?

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Exercise 76If there are �ve people in a room, what is the probability that at least two people have the samebirthday?

4 CONDITIONAL PROBABILITY

Do the following problems using the conditional probability formula: P (A | B) = P (A∩B)P (B) .

Exercise 77 (Solution on p. 18.)

A card is drawn from a deck. Find the conditional probability of P (a queen | a face card).

Exercise 78A card is drawn from a deck. Find the conditional probability of P (a queen | a club).

Exercise 79 (Solution on p. 18.)

A die is rolled. Find the conditional probability that it shows a three if it is known that an oddnumber has shown.

Exercise 80If P (A) = .3 and P (B) = .4, and P (A and B) = .12, �nd the following.

a. P (A | B)b. P (B | A)

The following table shows the distribution of Democratic and Republican U.S. Senators by gender.

MALE(M) FEMALE(F) TOTAL

DEMOCRATS(D) 39 4 43

REPUBLICANS(R) 52 5 57

TOTALS 91 9 100

Table 2

Use this table to determine the following probabilities:

Exercise 81 (Solution on p. 18.)

P (M | D) (60)

Exercise 82

P (D | M) (61)

Exercise 83 (Solution on p. 18.)

P (F | R) (62)

Exercise 84

P (R | F ) (63)

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Do the following conditional probability problems.

Exercise 85 (Solution on p. 18.)

At De Anza College, 20% of the students take Finite Math, 30% take History, and 5% takeboth Finite Math and History. If a student is chosen at random, �nd the following conditionalprobabilities.

a. He is taking Finite Math given that he is taking History.b. He is taking History assuming that he is taking Finite Math.

Exercise 86At a college, 60% of the students pass Accounting, 70% pass English, and 30% pass both of thesecourses. If a student is selected at random, �nd the following conditional probabilities.

a. He passes Accounting given that he passed English.b. He passes English assuming that he passed Accounting.

Exercise 87 (Solution on p. 19.)

If P (F ) = .4 and P (E | F ) = .3, �nd P (E and F ).

Exercise 88If P (E) = .3, and P (F ) = .3, and E and F are mutually exclusive, �nd P (E | F ).

Exercise 89 (Solution on p. 19.)

If P (E) = .6 and P (E and F ) = .24, �nd P (F | E).

Exercise 90If P (E and F ) = .04 and P (E | F ) = .1, �nd P (F ).

Consider a family of three children. Find the following probabilities.

Exercise 91 (Solution on p. 19.)

P (two boys | �rst born is a boy) (64)

Exercise 92

P (all girls | at least one girl is born) (65)

Exercise 93 (Solution on p. 19.)

P (children of both sexes | �rst born is a boy) (66)

Exercise 94

P (all boys | there are children of both sexes) (67)

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5 INDEPENDENT EVENTS

The distribution of the number of �ction and non-�ction books checked out at a city's main library and ata smaller branch on a given day is as follows.

MAIN(M) BRANCH(B) TOTAL

FICTION(F) 300 100 400

NON-FICTION(N) 150 50 200

TOTALS 450 150 600

Table 3

Use this table to determine the following probabilities:

Exercise 95 (Solution on p. 19.)

P (F ) (68)

Exercise 96

P (M | F ) (69)

Exercise 97 (Solution on p. 19.)

P (N | B) (70)

Exercise 98Is the fact that a person checks out a �ction book independent of the main library?

For a two-child family, let the events E, F , and G be as follows.E: The family has at least one boy F : The family has children of both sexes G: The family's �rst born

is a boy

Exercise 99 (Solution on p. 19.)

Find the following.

a. P (E)b. P (F )c. P (E ∩ F )d. Are E and F independent?

Exercise 100Find the following.

a. P (F )b. P (G)c. P (F ∩G)d. Are F and G independent?

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Do the following problems involving independence.

Exercise 101 (Solution on p. 19.)

If P (E) = .6, P (F ) = .2, and E and F are independent, �nd P (E and F ).

Exercise 102If P (E) = .6, P (F ) = .2, and E and F are independent, �nd P (E or F ).

Exercise 103 (Solution on p. 19.)

If P (E) = .9, P (F | E) = .36, and E and F are independent, �nd P (F ).

Exercise 104If P (E) = .6, P (E or F ) = .08, and E and F are independent, �nd P (F ).

Exercise 105 (Solution on p. 19.)

In a survey of 100 people, 40 were casual drinkers, and 60 did not drink. Of the ones who drank, 6had minor headaches. Of the non-drinkers, 9 had minor headaches. Are the events "drinkers" and"had headaches" independent?

Exercise 106It is known that 80% of the people wear seat belts, and 5% of the people quit smoking last year. If4% of the people who wear seat belts quit smoking, are the events, wearing a seat belt and quittingsmoking, independent?

Exercise 107 (Solution on p. 19.)

John's probability of passing statistics is 40%, and Linda's probability of passing the same courseis 70%. If the two events are independent, �nd the following probabilities.

a. P (both of them will pass statistics)b. P (at least one of them will pass statistics)

Exercise 108Jane is �ying home for the Christmas holidays. She has to change planes twice on the way home.There is an 80% chance that she will make the �rst connection, and a 90% chance that she willmake the second connection. If the two events are independent, �nd the following probabilities.

a. P (Jane will make both connections)b. P (Jane will make at least one connection)

For a three-child family, let the events E, F , and G be as follows.E: The family has at least one boy F : The family has children of both sexes G: The family's �rst born

is a boy

Exercise 109 (Solution on p. 19.)

Find the following.

a. P (E)b. P (F )c. P (E ∩ F )d. Are E and F independent?

Exercise 110Find the following.

a. P (F )b. P (G)c. P (F ∩G)d. Are F and G independent?

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6 CHAPTER REVIEW

Exercise 111 (Solution on p. 19.)

Two dice are rolled. Find the probability that the sum of the dice is

a. fourb. �ve

Exercise 112 (Solution on p. 19.)

A jar contains 3 red, 4 white, and 5 blue marbles. If a marble is chosen at random, �nd thefollowing probabilities:

a. P (red or blue)b. P (not blue)

Exercise 113 (Solution on p. 19.)

A card is drawn from a standard deck. Find the following probabilities:

a. P (a jack or a king)b. P (a jack or a spade)

Exercise 114 (Solution on p. 20.)

A basket contains 3 red and 2 yellow apples. Two apples are chosen at random. Find the followingprobabilities:

a. P (one red, one yellow)b. P (at least one red)

Exercise 115 (Solution on p. 20.)

A basket contains 4 red, 3 white, and 3 blue marbles. Three marbles are chosen at random. Findthe following probabilities:

a. P (two red, one white)b. P (�rst red, second white, third blue)c. P (at least one red)d. P (none red)

Exercise 116 (Solution on p. 20.)

Given a family of four children. Find the following probabilities:

a. P (All boys)b. P (1 boy and 3 girls)

Exercise 117 (Solution on p. 20.)

Consider a family of three children. Find the following:

a. P (children of both sexes | �rst born is a boy)b. P (all girls | children of both sexes)

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Exercise 118 (Solution on p. 20.)

Mrs. Rossetti is �ying from San Francisco to New York. On her way to the San Francisco Airportshe encounters heavy tra�c and determines that there is a 20% chance that she will be late to theairport and will miss her �ight. Even if she makes her �ight, there is a 10% chance that she willmiss her connecting �ight at Chicago. What is the probability that she will make it to New Yorkas scheduled?

Exercise 119 (Solution on p. 20.)

At a college, twenty percent of the students take history, thirty percent take math, and ten percenttake both. What percent of the students take at least one of these two courses?

Exercise 120 (Solution on p. 20.)

In a T-maze, a mouse may run to the right (R) or may run to the left (L). A mouse goes up themaze three times, and events E and F are described as follows:

E: Runs to the right on the �rst trialF : Runs to the left two consecutive timesDetermine whether the events E and F are independent.

Exercise 121 (Solution on p. 20.)

A college has found that 20% of its students take advanced math courses, 40% take advancedEnglish courses and 15% take both advanced math and advanced English courses. If a student isselected at random, what is the probability that

a. he is taking English given that he is taking math?b. he is taking math or English?

Exercise 122 (Solution on p. 20.)

If there are 35 students in a class, what is the probability that at least two have the same birthday?

Exercise 123 (Solution on p. 20.)

A student feels that her probability of passing accounting is .62, of passing mathematics is .45, andher passing accounting or mathematics is .85. Find the probability that the student passes bothaccounting and math.

Exercise 124 (Solution on p. 20.)

There are nine judges on the U. S. Supreme Court of which �ve are conservative and four liberal.This year the court will act on six major cases. What is the probability that out of six cases thecourt will favor the conservatives in at least four?

Exercise 125 (Solution on p. 20.)

Five cards are drawn from a deck. Find the probability of obtaining

a. four cards of a single suitb. two cards of one suit, two of another suit, and one from the remainingc. a pair(e.g. two aces and three other cards)d. a straight �ush(�ve in a row of a single suit but not a royal �ush)

Exercise 126 (Solution on p. 20.)

The following table shows a distribution of drink preferences by gender.

Coke(C) Pepsi(P) Seven Up(S) TOTALS

Males(M) 60 50 22 132

Females(F) 50 40 18 108

TOTALS 110 90 40 240

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Table 4

The events M , F , C, P and S are de�ned as Male, Female, Coca Cola, Pepsi, and Seven Up,respectively. Find the following:

a. P (F | S)b. P (P | F )c. P (C | M)d. P (M | P

⋃C)

e. Are the events F and S mutually exclusive?f. Are the events F and S independent?

Exercise 127 (Solution on p. 21.)

At a clothing outlet 20% of the clothes are irregular, 10% have at least a button missing and 4%are both irregular and have a button missing. If Martha found a dress that has a button missing,what is the probability that it is irregular?

Exercise 128 (Solution on p. 21.)

A trade delegation consists of four Americans, three Japanese and two Germans. Three people arechosen at random. Find the following probabilities:

a. P (two Americans and one Japanese)b. P (at least one American)c. P (One of each nationality)d. P (no German)

Exercise 129 (Solution on p. 21.)

A coin is tossed three times, and the events E and F are as follows.E: It shows a head on the �rst toss F : Never turns up a tailAre the events E and F independent?

Exercise 130 (Solution on p. 21.)

If P (E) = .6 and P (F ) = .4 and E and F are mutually exclusive, �nd P (E and F ).

Exercise 131 (Solution on p. 21.)

If P (E) = .5 and P (F ) = .3 and E and F are independent, �nd P (E⋃F).

Exercise 132 (Solution on p. 21.)

If P (F ) = .9 and P (E | F ) = .36 and E and F are independent, �nd P (E).

Exercise 133 (Solution on p. 21.)

If P (E) = .4 and P (E or F ) = .9 and E and F are independent, �nd P (F ).

Exercise 134 (Solution on p. 21.)

If P (E) = .4 and P (F | E) = .5, �nd P (E and F ).

Exercise 135 (Solution on p. 21.)

If P (E) = .6 and P (E and F ) = .3, �nd P (F | E).

Exercise 136 (Solution on p. 21.)

If P (E) = .3 and P (F ) = .4 and E and F are independent, �nd P (E | F ).

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Solutions to Exercises in this Module

Solution to Exercise (p. 1)

{1, 2, 3, 4, 5, 6} (71)

Solution to Exercise (p. 1)

{1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T} (72)

Solution to Exercise (p. 1)

1 2 3 4 5 6

1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

Table 5

Solution to Exercise (p. 1)

4/52 (73)

Solution to Exercise (p. 2)

13/52 (74)

Solution to Exercise (p. 2)

16/52 (75)

Solution to Exercise (p. 2)

6/20 (76)

Solution to Exercise (p. 2)

13/20 (77)

Solution to Exercise (p. 2)

3/8 (78)

Solution to Exercise (p. 3)

6/8 (79)

Solution to Exercise (p. 3)

4/36 (80)

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Solution to Exercise (p. 3)

7/36 (81)

Solution to Exercise (p. 3)

4/12 (82)

Solution to Exercise (p. 3)0Solution to Exercise (p. 4)YesSolution to Exercise (p. 4)NoSolution to Exercise (p. 4)NoSolution to Exercise (p. 5)

16/52 (83)

Solution to Exercise (p. 5)

13/36 (84)

Solution to Exercise (p. 5)40%Solution to Exercise (p. 6)

39/100 (85)

Solution to Exercise (p. 6)

95/100 (86)

Solution to Exercise (p. 6)

61/100 (87)

Solution to Exercise (p. 6)0Solution to Exercise (p. 6)0.5Solution to Exercise (p. 7)

20/56 (88)

Solution to Exercise (p. 7)

6/56 (89)

Solution to Exercise (p. 7)

1/6 (90)

Solution to Exercise (p. 7)

3/10 (91)

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OpenStax-CNX module: m38666 18

Solution to Exercise (p. 7)

10/220 (92)

Solution to Exercise (p. 8)

56/220 (93)

Solution to Exercise (p. 8)

45/1365 (94)

Solution to Exercise (p. 8)

21/1365 (95)

Solution to Exercise (p. 8)

324/1365 (96)

Solution to Exercise (p. 8)

79092/2, 598, 960 (97)

Solution to Exercise (p. 8)

24/2, 598, 960 (98)

Solution to Exercise (p. 8)

1, 584/2, 598, 960 (99)

Solution to Exercise (p. 8)0.973Solution to Exercise (p. 9)

4/12 (100)

Solution to Exercise (p. 9)

1/3 (101)

Solution to Exercise (p. 9)

39/43 (102)

Solution to Exercise (p. 9)5/57Solution to Exercise (p. 10)

a. 1/6b. 1/4

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OpenStax-CNX module: m38666 19

Solution to Exercise (p. 10)0.12Solution to Exercise (p. 10)0.4Solution to Exercise (p. 10)

2/4 (103)

Solution to Exercise (p. 10)

3/4 (104)

Solution to Exercise (p. 11)

2/3 (105)

Solution to Exercise (p. 11)

50/150 (106)

Solution to Exercise (p. 11)

a. 3/4b. 2/4c. 2/4d. no

Solution to Exercise (p. 12)0.12Solution to Exercise (p. 12)0.36Solution to Exercise (p. 12)YesSolution to Exercise (p. 12)

a. 28/100b. 82/100

Solution to Exercise (p. 12)

a. 7/8b. 6/8c. 6/8d. no

Solution to Exercise (p. 13)

a. 3/36b. 4/36

Solution to Exercise (p. 13)

a. 8/12b. 7/12

Solution to Exercise (p. 13)

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OpenStax-CNX module: m38666 20

a. 8/52b. 16/52

Solution to Exercise (p. 13)

a. 3/5b. 9/10

Solution to Exercise (p. 13)

a. 3/20b. 1/20c. 5/6d. 1/6

Solution to Exercise (p. 13)

a. 1/16b. 1/4

Solution to Exercise (p. 13)

a. 3/4b. 0

Solution to Exercise (p. 14)0.72Solution to Exercise (p. 14)40%Solution to Exercise (p. 14)independentSolution to Exercise (p. 14)

a. 3/4b. 0.45

Solution to Exercise (p. 14)0.8144Solution to Exercise (p. 14)0.22Solution to Exercise (p. 14)0.45278Solution to Exercise (p. 14)

a. 111540/2598960b. 949104/2598960c. 1349088/2598960d. 36/2598960

Solution to Exercise (p. 14)

a. 9/20b. 10/27c. 15/33d. 11/20e. no

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OpenStax-CNX module: m38666 21

f. yes

Solution to Exercise (p. 15)0.40Solution to Exercise (p. 15)

a. 3/14b. 37/42c. 2/7d. 35/84

Solution to Exercise (p. 15)NoSolution to Exercise (p. 15)0Solution to Exercise (p. 15)0.65Solution to Exercise (p. 15)0.36Solution to Exercise (p. 15)

5/6 (107)

Solution to Exercise (p. 15)0.2Solution to Exercise (p. 15)0.5Solution to Exercise (p. 15)0.3

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