Deck 9: Sequences Series and Probability

Question 1

Find the probability for the experiment of tossing a coin three times.Use the sample space
S = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}

The probability of getting exactly one tail.

A) $\frac { 3 } { 8 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 8 } { 3 }$
E) 2

Answer 1

$\frac { 3 } { 8 }$

Question 2

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = \frac { 6 } { 7 }$

A) $\frac { 6 } { 7 }$
B) $\frac { 5 } { 7 }$
C) $\frac { 4 } { 7 }$
D) $\frac { 3 } { 7 }$
E) $\frac { 1 } { 7 }$

Answer 2

$\frac { 1 } { 7 }$

Question 3

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.78$

A)0.37
B)0.22
C)0.78
D)0.27
E)0.32

Answer 3

0.22

Question 4

Find the probability for the experiment of tossing a six-sided die twice.
The sum is at least 8.

A) $\frac { 7 } { 12 }$
B) $\frac { 11 } { 12 }$
C) $\frac { 13 } { 19 }$
D) $\frac { 19 } { 12 }$
E) $\frac { 5 } { 12 }$

Question 5

There were approximately 28 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.What is the probability that a person selected at random from the population of unemployed workers is in the 45-64 age group.( $a = 28 \%$ and $b = 38 \%$ )

A) $\frac { 1 } { 38 }$
B) $\frac { 19 } { 50 }$
C) $\frac { 50 } { 19 }$
D)38
E) $\frac { 1 } { 100 }$

Question 6

You are given the probability that an event will not happen.Find the probability that the event will happen. $P \left( E ^ { \prime } \right) = 0.37$

A)0.73
B)0.63
C)0.83
D)0.68
E)0.78

Question 7

Find the probability for the experiment of tossing a coin four times.Use the sample space
S = {HHHH,HHHT,HHTH,HHTT,HTHH,HTTH,HTTT,THHH,THHH,THHT,THTH,THTT,TTHH,TTHT,TTTH,TTTT}

The probability of getting exactly one head.

A) $\frac { 8 } { 3 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 3 } { 8 }$
D) 4
E) $\frac { 1 } { 2 }$

Question 8

There were approximately 8.92 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.What is the probability that a person selected at random from the population of unemployed workers is in the 45-64 age group. ?

A) $\frac { 1 } { 100 }$
B) $\frac { 1 } { 50 }$
C) $\frac { 13 } { 50 }$
D) $\frac { 5 } { 3 }$
E)60

Question 9

Determine the sample space for the experiment. ​
A six-sided die is tossed twice and the sum of the results is recorded.
​

A)​{2,3,...,12}
B)​{3,4,...,6}
C)​{1,2,...,6}
D)​{1,2,...,6}
E)​{3,4,...,18}

Question 10

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = \frac { 1 } { 5 }$

A) $\frac { 9 } { 5 }$
B) $\frac { 3 } { 5 }$
C) $\frac { 1 } { 5 }$
D) $\frac { 2 } { 5 }$
E) $\frac { 4 } { 5 }$

Question 11

Find the probability for the experiment of tossing a coin two times.Use the sample space
S = {HH,HT,TH,TT}

The probability of getting exactly two tails.

A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 3 } { 8 }$
D) $\frac { 1 } { 3 }$
E) $\frac { 1 } { 8 }$

Question 12

Find the probability for the experiment of tossing a six-sided die twice.
The sum is 7.

A) $\frac { 36 } { 7 }$
B) $\frac { 1 } { 6 }$
C) $\frac { 1 } { 36 }$
D) $\frac { 7 } { 36 }$
E)6

Question 13

There were approximately 6.92 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.Estimate the number of unemployed workers in the 16-19 age group.(Round your answer to two decimal places.) ​ ​

A)2.97 million
B)4.97 million
C)1.97 million
D)0.97 million
E)3.97 million

Question 14

Find the probability for the experiment of tossing a six-sided die twice.
The sum is less than 4.

A)36
B) $\frac { 36 } { 13 }$
C) $\frac { 1 } { 12 }$
D) $\frac { 13 } { 36 }$
E) $\frac { 13 } { 36 }$ .

Question 15

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = \frac { 11 } { 35 }$

A) $\frac { 11 } { 35 }$
B) $\frac { 35 } { 24 }$
C) $\frac { 8 } { 35 }$
D) $\frac { 24 } { 35 }$
E) $\frac { 35 } { 11 }$

Question 16

You are given the probability that an event will not happen.Find the probability that the event will happen. $P \left( E ^ { \prime } \right) = 0.75$

A)0.4
B)0.25
C)0.35
D)0.3
E)0.45

Question 17

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.18$

A)0.88
B)0.89
C)0.82
D)0.87
E)0.18

Question 18

Find the probability for the experiment of selecting one card from a standard deck of 52 playing cards.
The card is a 7 or lower.(Aces are low.)

A) $\frac { 7 } { 52 }$
B) $\frac { 13 } { 7 }$
C) $\frac { 1 } { 7 }$
D) $\frac { 51 } { 52 }$
E) $\frac { 7 } { 13 }$

Question 19

Find the probability for the experiment of tossing a coin two times.Use the sample space $S = \{ H H , H T , T H , T T \}$ .
The probability of getting at least two heads.

A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 5 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 8 }$
E) $\frac { 1 } { 3 }$

Question 20

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) =$ $\frac { 17 } { 20 }$

A) $\frac { 20 } { 17 }$
B) $\frac { 3 } { 20 }$
C) $\frac { 17 } { 20 }$
D) $\frac { 1 } { 100 }$
E) $\frac { 20 } { 3 }$

Question 21

The educational attainment of a country population age 25 years or older in 2007 is shown in the circle graph.Use the fact that the population of people 25 years or older was approximately 8.1 million in 2007 and let $a = 8.1 \%$ , $b = 17.8 \%$ , $c = 9.8 \%$ and $d = 16 \%$ .Find the probability that a person 25 years or older selected at random has earned an Associate's degree or higher.

A)0.357
B)0.457
C)0.757
D)0.657
E)0.557

Question 22

A college sent a survey to a sample of juniors.Of the 512 students surveyed, 279 live on campus, of whom 110 have a GPA of 2.5 or greater.The other 233 juniors live off-campus, of whom 85 have a GPA of 2.5 or greater.What is the probability that a survey participant chosen at random lives on campus and has a GPA of 2.5 or greater?

A) $\frac { 279 } { 512 }$
B) $\frac { 22 } { 39 }$
C) $\frac { 110 } { 279 }$
D) $\frac { 195 } { 512 }$
E) $\frac { 55 } { 256 }$

Question 23

The educational attainment of a country population age 25 years or older in 2007 is shown in the circle graph.Use the fact that the population of people 25 years or older was approximately 293.32 million in 2007.Estimate the number of people 25 years or older who have high school diplomas.Round your anser to two decimal places. ​ ​

A)261.38 million
B)251.38 million
C)291.38 million
D)271.38 million
E)281.38 million

Question 24

The figure shows the results of a recent survey in which 1011 adults were asked to grade U.S.public schools.An adult is selected at random.What is the probability that the adult will give the U.S.public schools an A
( $a = 3 \%$ , $b = 11 \%$ , $c = 19 \%$ )

A) $\frac { 100 } { 3 }$
B) $\frac { 3 } { 100 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 3 } { 50 }$
E)100

Question 25

In a high school graduating class of 128 students, 52 are on the honor roll.Of these, 45 are going on to college; of the other 76 students, 53 are going on to college.A student is selected at random from the class.What is the probability that the person chosen is going to college. ?

A) $\frac { 49 } { 64 }$
B) $\frac { 64 } { 49 }$
C) $\frac { 53 } { 128 }$
D) $\frac { 128 } { 53 }$
E) $\frac { 45 } { 128 }$

Question 26

The figure shows the results of a survey in which auto racing fans listed their favorite type of racing.What is the probability that an auto racing fan selected at random does not list NHRA drag racing as his or her favorite type of racing
( $a = 55 \%$ , $b = 15 \%$ , $c = 13 \%$ , $d = 6 \%$ )

A) $\frac { 11 } { 20 }$
B) $\frac { 3 } { 20 }$
C) $\frac { 17 } { 20 }$
D) $\frac { 20 } { 3 }$
E) $\frac { 20 } { 17 }$

Question 27

A college sent a survey to a sample of juniors.Of the 620 students surveyed, 307 live on campus, of whom 139 have a GPA of 2.5 or greater.The other 313 juniors live off-campus, of whom 153 have a GPA of 2.5 or greater.What is the probability that a survey participant chosen at random has a GPA less than 2.5?

A) $\frac { 307 } { 620 }$
B) $\frac { 139 } { 620 }$
C) $\frac { 82 } { 155 }$
D) $\frac { 139 } { 292 }$
E) $\frac { 139 } { 307 }$

Question 28

The figure shows the results of a recent survey in which 1040 adults were asked to grade U.S.public schools.Estimate the number of adults who gave U.S.public schools a B. ​ ​

A)265
B)260
C)255
D)250
E)270

Question 29

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing 3 green, 5 yellow and 4 red marbles such that both marbles are yellow.

A) $\frac { 2 } { 5 }$
B) $\frac { 5 } { 7 }$
C) $\frac { 25 } { 144 }$
D) $\frac { 25 } { 132 }$
E) $\frac { 5 } { 33 }$

Question 30

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.8$

A)1
B)0.2
C)0.1
D)0.8
E)0

Question 31

The figure shows the results of a survey in which auto racing fans listed their favorite type of racing.What is the probability that an auto racing fan selected at random lists NASCAR racing as his or her favorite type of racing
( $a = 58 \%$ , $b = 14 \%$ )

A) $\frac { 18 } { 25 }$
B) $\frac { 5 } { 29 }$
C) $\frac { 29 } { 5 }$
D) $\frac { 50 } { 29 }$
E) $\frac { 29 } { 50 }$

Question 32

The figure shows the results of a recent survey in which 14 adults were asked to grade U.S.public schools.An adult is selected at random.What is the probability the adult will give the U.S.public schools a C or a D
( $a = 14 \%$ , $b = 50 \%$ )

A) $\frac { 16 } { 25 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 50 } { 7 }$
D) $\frac { 25 } { 16 }$
E) $\frac { 7 } { 50 }$

Question 33

Find the probability for the experiment of tossing a six-sided die twice such that the sum is either 7 or 11.

A) $\frac { 2 } { 9 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 6 }$
D) $\frac { 5 } { 16 }$
E) $\frac { 7 } { 36 }$

Question 34

The educational attainment of a country population age 25 years or older in 2007 is shown in the circle graph.Use the fact that the population of people 25 years or older was approximately 243.32 million in 2007.Estimate the number of people 25 years or older who have advanced degrees.Round your anser to two decimal places. ​ ​

A)24.09 million
B)64.09 million
C)44.09 million
D)54.09 million
E)34.09 million

Question 35

The educational attainment of a country population age 25 years or older in 2007 is shown in the circle graph.Use the fact that the population of people 25 years or older was approximately 8.0 million in 2007 and let $a = 8.0 \%$ , $b = 19.9 \%$ and $c = 9.5 \%$ .Find the probability that a person 25 years or older selected at random has earned a Bachelor's degree or higher.

A)0.294
B)1.294
C)4.294
D)2.294
E)3.294

Question 36

There were approximately 42 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.What is the probability that a person selected at random from the population of unemployed workers is 45 or older? ( $a = 42 \%$ and $b = 39 \%$ )

A) $\frac { 1 } { 100 }$
B) $\frac { 21 } { 50 }$
C) $\frac { 1 } { 42 }$
D) $\frac { 50 } { 21 }$
E)42

Question 37

The figure shows the results of a survey in which auto racing fans listed their favorite type of racing.What is the probability that an auto racing fan selected at random lists Formula One $d = 8 \%$ or motorcycle racing $c = 10 \%$ as his or her favorite type of racing
( $a = 53 \%$ , $b = 18 \%$ )

A) $\frac { 50 } { 9 }$
B) $\frac { 1 } { 50 }$
C)1
D) $\frac { 9 } { 50 }$
E) $\frac { 2 } { 25 }$

Question 38

You are given the probability that an event will not happen.Find the probability that the event will happen. $P ( E ) = \frac { 28 } { 40 }$

A) $\frac { 7 } { 10 }$
B) 1
C) $\frac { 3 } { 20 }$
D) 0
E) $\frac { 3 } { 10 }$

Question 39

The educational attainment of a country population age 25 years or older in 2007 is shown in the circle graph.Use the fact that the population of people 25 years or older was approximately 6.3 million in 2007 and let $a = 6.3 \%$ , $b = 20.5 \%$ , $c = 11.6 \%$ and $d = 13.3 \%$ .Find the probability that a person 25 years or older selected at random has earned a Bachelor's degree or higher.

A)3.321
B)2.321
C)4.321
D)0.321
E)1.321

Question 40

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing two green, five yellow, and three red marbles such that the marbles are different colors.

A) $\frac { 31 } { 90 }$
B) $\frac { 31 } { 15 }$
C) $\frac { 31 } { 45 }$
D) $\frac { 1 } { 5 }$
E) $\frac { 62 } { 9 }$

Question 41

In a sample of 20 hand-held calculators, 15 are known to be nonfunctional.If 7 of these calculators are selected at random, what is the probability that exactly 5 in the selection are nonfunctional? Round to the nearest thousandth.

A)0
B)0.714
C)0.387
D)0.467
E)0.750

Question 42

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, five yellow, and two red marbles such that the marbles are different colors.

A) $\frac { 31 } { 90 }$
B) $\frac { 31 } { 15 }$
C) $\frac { 31 } { 45 }$
D) $\frac { 1 } { 5 }$
E)0

Question 43

Determine the sample space for the experiment.
Two prize winners are selected from six people: A, B, C, D, E, and F.

A)S = {AB, AC, AD, AE, BC, BD, BE, CD, CE, DE}
B)S = {AB, AC, AD, AE, AF}
C)S = {AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF}
D)S = {AB, AC, AD, BC, BD, CD}
E)S = {AB, CD, EF}

Question 44

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing 2 green, 6 yellow and 3 red marbles such that both marbles are yellow.

A) $\frac { 1 } { 3 }$
B) $\frac { 6 } { 5 }$
C) $\frac { 36 } { 121 }$
D) $\frac { 18 } { 55 }$
E) $\frac { 3 } { 11 }$

Question 45

Determine the number of ways a computer can randomly generate two distinct integers whose sum is 13 from 1 through 17 in increasing order. ​

A)6
B)2
C)10
D)8
E)4

Question 46

Determine the number of ways a computer can randomly generate the integer that is divisible by 3 from 1 through 42.

A)18
B)12
C)10
D)16
E)14

Question 47

Determine the number of ways a computer can randomly generate the odd integers from 1 through 26. ​

A)11
B)15
C)17
D)13
E)9

Question 48

A college needs two additional faculty members: a chemist and a statistician.In how many ways can these positions be filled if there are three applicants for the chemistry position and four applicants for the statistics position?

A)10
B)11
C)16
D)14
E)12

Question 49

Find the probability for the experiment of selecting one card from a standard deck of 52 playing cards such that the card is a 10 or higher (aces are low).

A) $\frac { 3 } { 13 }$
B) $\frac { 5 } { 13 }$
C) $\frac { 1 } { 2 }$
D)1
E) $\frac { 4 } { 13 }$

Question 50

You are given the probability that an event will not happen.Find the probability that the event will happen. $P ( E ) = \frac { 4 } { 15 }$

A) $\frac { 4 } { 15 }$
B)0
C)1
D) $\frac { 11 } { 15 }$
E) $\frac { 11 } { 30 }$

Question 51

Ten people are boarding an aircraft.Two have tickets for first class and board before those in the economy class.In how many ways can the ten people board the aircraft? ​

A)240
B)48
C)80,640
D)12
E)1,440

Question 52

A college student is preparing a course schedule for the next semester.The student may select one of five mathematics courses, one of two science courses, and one of five courses from the social sciences and humanities.How many schedules are possible? ​

A)55
B)45
C)60
D)50
E)40

Question 53

Determine the number of ways a computer can randomly generate two distinct integers whose sum is 20 from 1 through 25 in increasing order. ​

A)7
B)5
C)11
D)13
E)9

Question 54

Determine the number of ways a computer can randomly generate the even integers from 1 through 30. ​

A)17
B)13
C)15
D)11
E)19

Question 55

Determine the number of ways a computer can randomly generate the prime integers from 1 through 40. A prime integer

A)10
B)14
C)12
D)8
E)16

Question 56

Determine the sample space for the experiment.
Three prize winners are selected from six people: A, B, C, D, E, and F.

Question 57

Determine the number of ways a computer can randomly generate the integers that is divisible by 4 from 1 through 40.

A)14
B)12
C)10
D)6
E)8

Question 58

Determine the number of ways a computer can randomly generate the integers that is greater than 8 from 1 through 12.

A)8
B)6
C)0
D)4
E)2

Question 59

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.87$

A)0.87
B)0.13
C)0.065
D)0
E)1

Question 60

A customer can choose one of two amplifiers, one of three compact disc players, and one of five speaker models for an entertainment system.Determine the number of possible system configurations. ​

A)40
B)35
C)​30
D)25
E)20

Question 61

How many three-digit numbers can be formed under the following condition? ​
The leading digit cannot be zero.
​

A)800
B)​500
C)​900
D)​600
E)​700

Question 62

In how many ways can a 22-question true-false exam be answered? (Assume that no questions are omitted.) ​

A)4,194,299
B)484
C)4,194,294
D)4,194,314
E)​4,194,304

Question 63

In how many ways can a seven-question true-false exam be answered? (Assume that no questions are omitted.) ​

A)138
B)128
C)133
D)118
E)123

Question 64

Eight sprinters have qualified for the finals in the 100-meter dash at the NCAA national track meet.In how many ways can the sprinters come in first, second, and third? (Assume there are no ties.) ​

A)486
B)386
C)436
D)336
E)536

Question 65

There are six processes involved in assembling a product, and these processes can be performed in any order.The management wants to test each order to determine which is the least time-consuming.How many different orders will have to be tested? ​

A)1,220
B)720
C)770
D)820
E)1,720

Question 66

How many four-digit numbers can be formed under the following condition? ​
The leading digit cannot be zero and the number must be less than 7,000.
​

A)5,800
B)6,000
C)5,700
D)5,600
E)5,900

Question 67

From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer will be filled.In how many different ways can the offices be filled? ​

A)12,380
B)13,380
C)12,880
D)13,880
E)11,880

Question 68

Evaluate ${ } _ { n } P _ { r }$ . ${ } _ { 19 } P _ { 2 }$

A)420
B)380
C)342
D)462
E)171

Question 69

Evaluate ${ } _ { n } P _ { r }$ . ${ } _ { 7 } P _ { 4 }$

A)5,040
B)1,680
C)3,024
D)35
E)840

Question 70

How many three-digit numbers can be formed under the following condition? ​
The leading digit cannot be zero and the number must be even.
​

A)900
B)450
C)350
D)400
E)550

Question 71

In how many ways can seven people sit in a seven-passenger car? ​

A)6,040
B)5,090
C)5,040
D)5,140
E)5,540

Question 72

Evaluate ${ } _ { n } P _ { r }$ . $100 P _ { 5 }$

A)94,109,400
B)970,200
C)75,287,520
D)9,034,502,400
E)858,277,728,000

Question 73

How many three-digit numbers can be formed under the following condition? ​
The number is at least 400.
​

A)590
B)610
C)620
D)580
E)600

Question 74

Evaluate ${ } _ { n } P _ { r }$ .
${ } _ { 7 } P _ { 3 }$

A)210
B)336
C)720
D)35
E)504

Question 75

Evaluate ${ } _ { n } P _ { r }$ . $100 P _ { 3 }$

A)94,109,400
B)161,700
C)970,200
D)858,277,728,000
E)9,034,502,400

Question 76

A baseball coach is creating a nine-player batting order by selecting from a team of 19 players.How many different batting orders are possible? ​

A)33,522,128,640
B)33,523,128,640
C)33,522,628,640
D)33,572,128,640
E)33,532,128,640

Question 77

Evaluate ${ } _ { n } P _ { r }$ . ${ } _ { 2 } P _ { 2 }$

A)2
B)20
C)30
D)6
E)12

Question 78

In how many ways can seven children posing for a photograph line up in a row? ​

A)5,040
B)5,140
C)5,090
D)6,040
E)5,540

Question 79

Evaluate ${ } _ { n } P _ { r }$ . ${ } _ { 16 } P _ { 8 }$

A)57,657,600
B)524,160
C)5,765,760
D)518,918,400
E)12,870

Question 80

Evaluate ${ } _ { n } P _ { r }$ . $40 P _ { 5 }$

A)2,193,360
B)658,008
C)59,280
D)78,960,960
E)2,763,633,600