Deck 11: Statistics

Question 1

A card is drawn from a deck and then replaced. Then, a second card is drawn. Find the probability of getting an ace both times.

Answer 1

1/169

Question 2

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a red card.

Answer 2

1/2

Question 3

If a die is rolled one time, find the probability of getting a number less than 4 and an even number.

Answer 3

1/6

Question 4

(a) the student did not answer the question. (b) the student is a girl or answered "No." (c) the student is a boy or answered "Yes."

Question 5

Three coins are tossed. Find the probability that exactly two coins land tails up.

Question 6

If a die is rolled one time, find the probability of getting a 3.

Question 7

Two dice are rolled. Find the probability of getting a sum of 3 or 8.

Question 8

In a certain geographic area, 19% of the inhabitants are under thirty. If four inhabitants are selected at random, what is the probability that all will be under thirty?

Question 9

A card is selected from an ordinary deck. Find the probability that the card was a diamond given that it was a 8.

Question 10

In a class of 20 students, there are 12 girls and 8 boys. Three students are selected to be teacher's assistants. Find the probability that the group consists of all girls.

Question 11

A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random, what is the probability that it is green?

Question 12

Six balls are numbered 1 through 6 and placed in a box. Two balls are selected without replacement. Find the probability that (a) the sum of the numbers is even. (b) the number on the second ball is less than the number on the first ball. (c) the sum of the numbers on both balls is greater than 5.

Question 13

How many ways can a committee of 5 people be selected from a group of 12 people?

Question 14

Find the probability of selecting 2 math books and 3 history books from a stack that contains 5 math books and 9 history books if the books are selected at random.

Question 15

In a classroom, the students are 4 boys and 2 girls. If one student is selected at random, find the probability that the student is a boy.

Question 16

Four red cards are numbered 1, 2, 3, and 4. Three black cards are numbered 5, 6, and 7. The cards are placed in a box and one card is selected at random. What is the probability that a red card was selected given that the number on the card was an even number?

Question 17

Three cards are drawn from a deck without replacement. Find the probability that (a) all are aces (b) all are hearts (c) all are black cards

Question 18

Tickets for a drawing are sold for $20 each. The holder of the winning ticket wins a cash prize of $3000. If 2000 tickets are sold, find the expected value of the gain.

Question 19

When two dice are tossed, find the odds in favor of getting a sum of 10.

Question 20

The odds in favor of an event are 1:5. Find the probability that the event will occur.

Question 21

How many different ways can a college select three applicants for a teaching position from a pool of 20 applicants?

Question 22

How many different ways can 7 people stand in line at a cash register?

Question 23

When two dice are tossed, find the odds against getting a sum of 2.

Question 24

How many ways can a person select four books, two CDs, and one DVD from ten books, twenty CDs, and five DVDs?

A) 199,500
B) 6,724,520
C) 405
D) 8,000

Question 25

Question 26

In a class of 20 students, there are 12 girls and 8 boys. Three students are selected to be teacher's assistants. Find the probability that the group consists of one girl and two boys.

Question 27

A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random, what is the probability that it is not yellow?

Question 28

At a community college, there are 6 English instructors, 5 math instructors, and history instructors. If one of these instructors is selected at random to serve on a committee, find the probability that the instructor is an English instructor or a history instructor.

Question 29

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a 2 or a king.

Question 30

Three coins are tossed. Find the probability that at least one coin lands heads up.

Question 31

A babysitter has four lollipops of different colors. In how many ways can she give onelollipop to each of the four children she is watching?

Question 32

Two dice are rolled. Find the probability that the sum was a 9 given that one of the numbers was a 4.

A) 1/11
B) 1/12
C) 1/6
D) 2/11

Question 33

Three coins are tossed. Find the probability that two or more coins land heads up.

Question 34

Draw a tree diagram to determine the sample space when three coins are tossed.

Question 35

Two dice are rolled. Find the probability of getting a sum less than or equal to 4.

Question 36

Question 37

Evaluate 0!

Question 38

The 825 children at a certain school were asked what they prefer to drink with their lunch, and the following responses were obtained.
$\begin{array}{c|c}\text { Drink } & \text { Percentage } \\\hline \text { soft drinks } & 354 \\\text { milk/chocolate milk } & 217 \\\text { water } & 97 \\\text { tea } & 34 \\\text { other } & 123\end{array}$

The school only serves milk, chocolate milk, or water with lunch. What is the probability that the first student in line for lunch will be served their preferred beverage with their lunch? Round to two decimal places.

A) 0.47
B) 0.38
C) 0.62
D) 0.53

Question 39

A person rolls two dice and wins if the sum is 7. What are the odds in favor of winning? What are the odds against winning?

Question 40

If a 40-year-old buys a $1500 life insurance policy at a cost of $50 and has a probability of 0.992 of living to age 41, find the expectation of the policy until the person reaches 41.

Question 41

A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random, what is the probability that it is yellow?

A) 1
B) 3/8
C) 3/16
D) 1/3

Question 42

Find the probability of getting any triple-digit number where all the digits are the same in a lottery game that consists of picking a three-digit number using the digits 1 to 6. Round to three decimal places, if necessary.

A) 0.005
B) 0.028
C) 0.008
D) 0.167

Question 43

A teacher has 12 boys and 19 girls in her class. In how many ways can she select 8 of the children to be in a play if she must select 4 boys and 4 girls.

A) 1,918,630
B) 1,918,640
C) 1,918,620
D) 1,918,610

Question 44

Find the probability using the binary probability formula. Round to four decimal places, if necessary. n = 14, p = 0.56, x = 4

A) 0.0037
B) 0.0268
C) 0.6426
D) 0.0001

Question 45

Three coins are tossed. Find the probability that no more than one coin lands heads up.

A) 5/8
B) 1/2
C) 1/4
D) 3/8

Question 46

The odds against an event are 4:10. Find the probability that the event will occur.

Question 47

A box contains eight $1 bills, five $5 bills, six $10 bills, and nine $20 bills. What is the expectation if one bill is selected?

A) $8.75
B) $9.75
C) $10.75
D) $11.75

Question 48

How many 3-digit codes using the digits 0 through 9 are possible if repetitions are allowed?

A) 729
B) 504
C) 1000
D) 30

Question 49

A baseball pitcher has only three pitches: a fast ball, a curve ball, and a knuckle ball. As the pitcher warms up before an inning, she wants to throw a fast ball 6 times, a curve ball 2 times, and a knuckle ball 3 times. How many different ways can this be done.

A) 11
B) 36
C) 1,108,800
D) 4620

Question 50

A single card is drawn from a deck. Find the probability of selecting a 9 or a spade.

A) 4/13
B) 9/26
C) 17/52
D) 7/52

Question 51

If a die is rolled one time, find the probability of getting a number less than 4 or an even number.

A) 1
B) 5/6
C) 1/6
D) 0

Question 52

A single card is drawn from a deck. What is the probability of getting a queen or a king?

A) 2/13
B) 7/52
C) 1/13
D) 3/52

Question 53

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a red 6.

A) 1/26
B) 1/4
C) 1/52
D) 1/13

Question 54

Question 55

Evaluate the expression. (4!)(2!)

A) 720
B) 40,320
C) 26
D) 48

Question 56

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a heart and an ace.

A) 1/13
B) 1/26
C) 1/52
D) 4/13

Question 57

A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random, what is the probability that it is not blue?

A) 1/11
B) 5/16
C) 11/16
D) 1/5

Question 58

On a survey at a particular university, 50% of the students indicated that they have misplaced their Student Identification Card at least once in the past year. If 10 students are in a campus computer lab, what is the probability that 2 or 3 of them have misplaced their Student Identification Card in the past year? Round to four decimal places, if necessary.

A) 0.791
B) 0.1611
C) 0.1875
D) 0.1465

Question 59

Two dice are rolled. Find the probability of getting a sum greater than 8.

A) 2/9
B) 13/36
C) 0
D) 5/18

Question 60

Evaluate the expression.
$$\frac { 10 ! } { 5 ! 2 ! }$$

A) 2
B) 15,120
C) 720
D) 1

Question 61

Two dice are rolled. Find the probability of getting a sum of 6.

A) 1/18
B) 1/6
C) 5/36
D) 1/9

Question 62

When a single card is drawn from a shuffled deck of cards, find the odds in favor of getting a 9.

A) 12:1
B) 1:51
C) 1:12
D) 51:1

Question 63

Decide whether the probability described is classical or empirical.
A container contains 50 ping pong balls labeled 1 through 50 . The probability of drawing a ball at random having a number 8 or less is $\frac { 4 } { 25 }$

A) classical
B) cannot be determined
C) empirical

Question 64

If a die is rolled one time, find the probability of getting a number greater than 1.

A) 1
B) 2/3
C) 5/6
D) 0

Question 65

Decide whether the selection described is a combination or a permutation. Two prizes are given to the winners of a race.

A) permutation
B) cannot be determined
C) combination

Question 66

In a classroom, the students are 6 boys and 5 girls. If one student is selected at random, find the probability that the student is a girl.

Question 67

Of all the students at a particular university, 14% prefer to have their first class at 8:00 am. If 7 students are waiting to be advised, what is the probability that exactly 5 of them prefer to have their first class at 8:00 am? Round to four decimal places, if necessary.

A) 0.0002
B) 0.1002
C) 0.0006
D) 0.0008

Question 68

Two dice are rolled. Find the probability of getting a 5 on one die or on both dice.

A) 7/18
B) 11/36
C) 1/3
D) 1/6

Question 69

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a king of diamonds.

A) 1/26
B) 1/4
C) 1/13
D) 1/52

Question 70

A package contains 6 candy canes, 2 of which are cracked. If 2 are selected, find the probability of getting no cracked candy canes.

A) 0.4000
B) 0.6037
C) 0.5105
D) 0.7019

Question 71

A coin is tossed and then a die is rolled. Find the probability of getting a 5 on the die given that the coin landed tails up.

A) 1/3
B) 1/12
C) 1/6
D) 1/36

Question 72

Question 73

If two people are selected at random, what is the probability that they were both born in May?

A) 1/132
B) 1/144
C) 1/12
D) 1/6

Question 74

How many different ways can 3 winning tickets be selected from 50 tickets, without replacement, if each ticket wins a different prize? (Note: the tickets can be selected in any order.)

A) 118,100
B) 117,700
C) 117,500
D) 117,600

Question 75

Question 76

How many different three letter permutations can be formed from the letters in the word clipboard?

A) 336
B) 504
C) 544,320
D) 729

Question 77

Decide whether the selection described is a combination or a permutation. Five club members are chosen to serve on a committee.

A) combination
B) cannot be determined
C) permutation

Question 78

If the odds against a horse winning a race are 7:3, what is the probability that the horse will win the race?

Question 79

A lottery has one $2000 prize, two $1000 prizes, and ten $500 prizes. Two thousand tickets are sold at $5 each. Find the expectation if a person buys two tickets.

A) -$1.00
B) -$0.25
C) -$0.50
D) -$2.00

Question 80

The bookstore has eight red school jerseys, ten blue school jerseys, and five green school jerseys to choose from. If a student selects one at random, find the probability it is red or green.