Deck 9: Probability

Question 1

An 8-sided die is rolled. The sides contain the numbers 1, 2, 3, 4, 5, 6, 7, 8. List the sample space of rolling one die.

A)None of these
B){8}
C){64}
D){1, 2, 3, 4, 5, 6, 7, 8}

Answer 1

D

Question 2

If a single card is drawn from a standard 52-card deck, in how many ways could it be a diamond or a face card?

A)13
B)25
C)22
D)21

Answer 2

C

Question 3

Determine whether the players have equal probabilities of winning.
Draw a card from a regular deck. If a club is drawn, player 1 wins; if a diamond is drawn, player 2 wins.

A)Yes
B)No

Answer 3

A

Question 4

Determine whether the players have equal probabilities of winning.
Draw a card from a regular deck. If a spade is drawn, player 1 wins; if a diamond is drawn, player 2 wins; otherwise player 3 wins.

A)Yes
B)No

Question 5

Determine the number of outcomes as requested.
Two 6-sided dice are thrown. Determine the number of ways that a score of either 3 or 4 can be obtained.

A)5
B)4
C)2
D)3

Question 6

A 6-sided die is rolled. The sides contain the numbers 1, 2, 3, 4, 5, 6. List the sample space of rolling one die.

A){6}
B){36}
C)None of these
D){1, 2, 3, 4, 5, 6}

Question 7

Determine the number of outcomes as requested.
Two 6-sided dice are thrown. Determine the number of ways that a score of less than 4 can be obtained.

A)6
B)3
C)4
D)2

Question 8

A box contains 3 blue cards numbered 1 through 3, and 4 green cards numbered 1 through 4. List the sample space of picking a blue card followed by a green card.

A){(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (4, 3)}
B){7}
C){12}
D){(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)}

Question 9

Give the number of possible outcomes for choosing a 4-digit number if each digit is chosen at random. The first digit may be a zero. Repetition is allowed.

A)10,000
B)40
C)1000
D)100,000

Question 10

Determine the number of outcomes as requested.
Two 6-sided dice are thrown. Determine the number of ways that a score of 8 can be obtained.

A)3
B)4
C)1
D)5

Question 11

A group of 15 people is assigned numbers 1 through 15. List the sample space of the event choosing a person with a number 5 or less.

A){1, 2, 3, 4, 5}
B){15}
C){1, 2, 3, 4}
D){1}

Question 12

Determine whether the players have equal probabilities of winning.
Draw a card from a regular deck. If a face card is drawn, player 1 wins; if a numbered card is drawn, player 2 wins.

A)Yes
B)No

Question 13

If a single card is drawn from a standard 52-card deck, in how many ways could it be an ace or a spade?

A)4
B)17
C)1
D)16

Question 14

A box contains 13 white cards numbered 1 through 13. List the sample space of the event choosing one card with a number greater than 6.

A){6, 7, 8, 9, 10, 11, 12, 13}
B){11}
C){7, 8, 9, 10, 11, 12, 13}
D){1, 2, 3, . . ., 13}

Question 15

Determine the number of outcomes as requested.
Two 6-sided dice are thrown. Determine the number of ways that a score which is a multiple of 3 can be obtained.

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

Question 16

A box contains 10 red cards numbered 1 through 10. List the sample space of picking one card from the box.

A){10}
B){1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
C){100}
D)None of these

Question 17

How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not allowed?

A)5
B)6
C)180
D)343

Question 18

A box contains 2 blue cards numbered 1 through 2, and 3 green cards numbered 1 through 3. List the sample space of picking a blue card followed by a green card.

A){12}
B){7}
C){(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3)}
D){(1,1), (1,2), (2, 1), (2, 2), (3, 1), (3, 2)}

Question 19

How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions of digits are allowed?

A)1000
B)899
C)27
D)900

Question 20

A lottery uses balls numbered 1 through 33. List the sample space of the event picking one even-numbered ball.

A){2}
B){2, 4, 6, . . ., 32}
C){1, 2, 3, . . ., 33}
D){32}

Question 21

Find the probability.
Two dice are rolled. Find the probability that the score on the dice is an even number.

Question 22

Find the probability.
Two dice are rolled. Find the probability that the score on the dice is at least 10.

Question 23

Find the probability.
Two dice are rolled. Find the probability that the score on the dice is 11.

Question 24

Toss two fair dice numbered 1 through 6. If the sum is 7, player 1 wins; if the sum is 3 or 4, player 2 wins.

A)Yes
B)No

Question 25

Toss two fair dice numbered 1 through 6. If the sum is even, player 1 wins; if the sum is odd, player 2 wins.

A)Yes
B)No

Question 26

Find the probability.
Two dice are rolled. Find the probability that the sum is odd and the number on one of the dice is a 1.

Question 27

Find the probability.
Two dice are rolled. Find the probability that the score on the dice is no more than 3.

Question 28

Toss two fair dice numbered 1 through 6. If the sum is 4, player 1 wins; if the sum is 10, player 2 wins.

A)Yes
B)No

Question 29

Find the probability.
Two dice are rolled. Find the probability that the score on the dice is 5 or that the dice both show the same number ("doubles").

Question 30

Find the probability.
Two dice are rolled. Find the probability that the score on the dice is 5.

Question 31

Determine whether the players have equal probabilities of winning.
Draw two cards from a regular deck. If cards of the same suit are drawn, player 1 wins; if cards of the same color are drawn, player 2 wins.

A)Yes
B)No

Question 32

Determine whether the players have equal probabilities of winning.
Draw two cards from a regular deck. If cards of the same suit are drawn, player 1 wins; if cards of the same number are drawn, player 2 wins.

A)Yes
B)No

Question 33

Toss two fair dice numbered 1 through 6. If the sum is 3, 5, 10, or 12, player 1 wins; if the sum is 2, 4, 9, or 11, player 2 wins.

A)Yes
B)No

Question 34

When a single card is drawn from an ordinary 52-card deck, find the probability of getting a red card.

Question 35

Find the probability.
Two dice are rolled. Find the probability that the score on the dice is either 5 or 10.

Question 36

When a single card is drawn from an ordinary 52-card deck, find the probability of getting a club.

Question 37

Find the probability.
Two dice are rolled. Find the probability that the score on the dice is either 8 or at most 3.

Question 38

When a single card is drawn from an ordinary 52-card deck, find the probability of getting a jack.

Question 39

When a single card is drawn from an ordinary 52-card deck, find the probability of getting a black 7.

Question 40

Toss two fair dice numbered 1 through 6. If the sum is 3, player 1 wins; if the sum is 12, player 2 wins.

A)Yes
B)No

Question 41

Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 5, 6, or 4?

Question 42

If you are dealt two cards successively (without replacement)from a standard 52-card deck, find the probability of getting two black cards.

Question 43

A bag contains 13 balls numbered 1 through 13. What is the probability of selecting a ball that has an even number?

Question 44

A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or a 8?

Question 45

If you are dealt two cards successively (with replacement of the first)from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second.

Question 46

A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a 7?

Question 47

When a single card is drawn from an ordinary 52-card deck, find the probability of getting the 7 of diamonds.

Question 48

One digit from the number 3,474,554 is written on each of seven cards. What is the probability of drawing a card that shows 5?

Question 49

A spinner has regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3?

Question 50

One digit from the number 9,848,778 is written on each of seven cards. What is the probability of drawing a card that shows 9, 8, or 4?

Question 51

Container A has balls numbered 1 through 8. Container B has balls numbered 1 through 4. What is the probability that a 4 is drawn from A followed by a 2 from B?

Question 52

One digit from the number 8,565,335 is written on each of seven cards. What is the probability of drawing a card that shows 8 or 3?

Question 53

A bag contains 9 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of choosing a blue marble?

Question 54

Construct a tree diagram that shows all possible outcomes when two coins are tossed.

A)
B)
C)
D)

Question 55

A bag contains 8 red marbles, 2 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue?

Question 56

Construct a tree diagram that shows all possible 2 -letter code words using only the letters x and y with repetition allowed.

A)
B)
C)
D)

Question 57

Construct a tree diagram that shows all possible 2 -letter code words using only the letters c and d without repetition.

A)
B)
C)
D)

Question 58

Construct a tree diagram that shows all possible 3-letter code words using only the letters p, q, and r without repetition.

Question 59

A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 3?

Question 60

When a single card is drawn from an ordinary 52-card deck, find the probability of getting a black 9 or a black 7.

Question 61

The first marble is blue and the second marble is red.

Question 62

Both marbles are green.

Question 63

One marble is green and one marble is red.

Question 64

Find the requested probability.
A box contains the eleven letters, MISSISSIPPI. Four letters are drawn one by one with replacement and recorded in order. What is the probability that the outcome is SIPS?

Question 65

The first marble is red and the second marble is white.

Question 66

Construct a tree diagram that shows all possible 2-letter code words using only the letters w, x, and y with no repetitions.

Question 67

Find the requested probability.
A box contains the six letters SAMPLE. Four letters are drawn one by one with replacement and recorded in order. What is the probability that the outcome is LEAP?

Question 68

The first marble is blue and the second marble is white.

Question 69

Three coins are tossed. Use the tree diagram to count how many ways the outcome consists of two heads and one tail.

Question 70

Juanita can choose a white, a red, or a black blouse, and a gray or a cream skirt. Construct a tree diagram that shows all possible skirt and blouse outfits that Juanita could select.

Question 71

Use the tree diagram to count how many four-child families have two boys and two girls.

Question 72

One marble is white and one marble is blue.

Question 73

The first marble is white and the second marble is blue.

Question 74

Both marbles are white.

Question 75

Find the requested probability.
A box contains the following mixture of colored marbles: 2 black, 3 red, 5 yellow, and 2 green. If two marbles are drawn, the second being drawn after the first is replaced, then what is the
Probability that both are black?

Question 76

Find the requested probability.
A box contains the eleven letters PROBABILITY. Four letters are drawn one by one with replacement and recorded in order. What is the probability that the outcome is TAIL?

Question 77

Clark is selecting new eyeglasses. He can choose styles A, B, or C in either the color black or orange. Construct a tree diagram that shows all possible choices that Clark can make.

Question 78

Both marbles are red.

Question 79

The first marble is blue and the second marble is blue.

Question 80

Construct a tree diagram that shows all possible outcomes when three coins are tossed.