Question 1

Find the probability.
-A 6-sided die is rolled. What is the probability of rolling a number less than $6 ?$
A) $\frac { 1 } { 3 }$

B) $\frac { 5 } { 7 }$

C) $\frac { 1 } { 6 }$

D) $\frac { 5 } { 6 }$

Accepted Answer

The numbers less than 6 on a 6-sided die are 1, 2, 3, 4, and 5, totaling 5 possibilities out of 6. Therefore, the probability is $\frac{5}{6}$.

Question 2

List the elements in the sample space of the experiment.
-A group of 13 people are assigned numbers 1 through 13 . List the sample space of the event choosing a person with a number 5 or less.
A) $\{ 1,2,3,4,5 \}$
B) $\{ 1 \}$
C) $\{ 1,2,3,4 \}$
D) $\{ 13 \}$

Accepted Answer

The sample space of choosing a person with a number 5 or less includes all numbers from 1 to 5, hence $\{ 1,2,3,4,5 \}$.

Question 3

Find the probability.
-Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 5 ?
A) 4
B) $\frac { 1 } { 9 }$

C) $\frac { 8 } { 9 }$

D) $\frac { 5 } { 6 }$

Accepted Answer

The possible outcomes for rolling two dice that sum to 5 are (1,4), (2,3), (3,2), and (4,1), totaling 4 outcomes. Since there are 36 possible outcomes when rolling two dice (6 sides each), the probability is $ \frac{4}{36} = \frac{1}{9} $.

Question 4

List the elements in the sample space of the experiment.
-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) $\{ 7 \}$
B) $\{ ( 1,1 ) , ( 1,2 ) , ( 1,3 ) , ( 2,1 ) , ( 2,2 ) , ( 2,3 ) \}$
C) $\{ ( 1,1 ) , ( 1,2 ) , ( 2,1 ) , ( 2,2 ) , ( 3,1 ) , ( 3,2 ) \}$
D) $\{ 12 \}$

Accepted Answer

The sample space for picking a blue card followed by a green card includes all possible combinations of the two events. Since there are 2 blue cards (numbered 1 and 2) and 3 green cards (numbered 1, 2, and 3), the sample space consists of all pairs where the first number represents the blue card and the second number represents the green card, resulting in 6 possible outcomes: $\{ ( 1,1 ) , ( 1,2 ) , ( 1,3 ) , ( 2,1 ) , ( 2,2 ) , ( 2,3 ) \}$.

Question 5

List the elements in the sample space of the experiment.
-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) $\{ 11 \}$
B) $\{ 7,8,9,10,11,12,13 \}$
C) $\{ 6,7,8,9,10,11,12,13 \}$
D) $\{ 1,2,3 , \ldots 13 \}$

Accepted Answer

The sample space for choosing a card with a number greater than 6 from cards numbered 1 through 13 includes the numbers 7, 8, 9, 10, 11, 12, and 13.

Question 6

Solve the problem.
-What are the odds in favor of spinning an A on this spinner? 
A) 4 to 2
B) 6 to 2
C) 2 to 6
D) 3 to 5

Accepted Answer

The answer of Solve the problem.
-What are the odds in...

Question 7

List the elements in the sample space of the experiment.
-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) $\{ 64 \}$
C) $\{ 8 \}$
D) $\{ 1,2,3,4,5,6,7,8 \}$

Accepted Answer

The sample space of rolling an 8-sided die is the set of all possible outcomes, which are the numbers $1,2,3,4,5,6,7,8$.

Question 8

Find the probability.
-A bag contains 13 balls numbered 1 through 13 . What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?
A) $\frac { 13 } { 6 }$

B) 6

C) $\frac { 6 } { 13 }$

D) $\frac { 2 } { 13 }$

Accepted Answer

There are 6 even numbers (2, 4, 6, 8, 10, 12) out of 13 total numbers, so the probability is $\frac{6}{13}$.

Question 9

Find the probability.
-A bag contains 3 red marbles, 2 blue marbles, and 8 green marbles. What is the probability of choosing a blue marble when one marble is drawn?
A) $\frac { 3 } { 13 }$
B) $\frac { 8 } { 13 }$
C) $\frac { 2 } { 5 }$
D) $\frac { 2 } { 13 }$

Accepted Answer

The total number of marbles is 3 + 2 + 8 = 13. There are 2 blue marbles, so the probability of choosing a blue marble is $\frac{2}{13}$.

Question 10

List the elements in the sample space of the experiment.
-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) $\{ 12 \}$
B) $\{ ( 1,1 ) , ( 1,2 ) , ( 1,3 ) , ( 1,4 ) , ( 2,1 ) , ( 2,2 ) , ( 2,3 ) , ( 2,4 ) , ( 3,1 ) , ( 3,2 ) , ( 3,3 ) , ( 3,4 ) \}$
C) $\{ 7 \}$
D) $\{ ( 1,1 ) , ( 1,2 ) , ( 1,3 ) , ( 2,1 ) , ( 2,2 ) , ( 2,3 ) , ( 3,1 ) , ( 3,2 ) , ( 3,3 ) , ( 4,1 ) , ( 4,2 ) , ( 4,3 ) \}$

Accepted Answer

Each blue card (3 options) can be paired with each green card (4 options), resulting in 3x4=12 unique pairs, correctly listed in option B.

Question 11

Find the probability.
-A lottery game contains 22 balls numbered 1 through 22 . What is the probability of choosing a ball numbered 23?
A) 1
B) 22
C) 0
D) $\frac { 1 } { 22 }$

Accepted Answer

Since there are no balls numbered 23 in the game, the probability of choosing a ball numbered 23 is 0.

Question 12

Find the probability.
-Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10 ?
A) $\frac { 5 } { 18 }$

B) $\frac { 1 } { 12 }$

C) 3

D) $\frac { 1 } { 18 }$

Accepted Answer

The only sums greater than 10 that can be rolled with two 6-sided dice are 11 and 12. The combinations that give these sums are (5,6), (6,5) for 11, and (6,6) for 12, making a total of 3 successful outcomes. Since there are 36 possible outcomes (6 sides on the first die times 6 sides on the second die), the probability is $ \frac{3}{36} = \frac{1}{12} $.

Question 13

List the elements in the sample space of the experiment.
-A lottery uses balls numbered 1 through 35 . List the sample space of the event picking one even-numbered ball.
A) $\{ 1,2,3 , \ldots , 35 \}$
B) $\{ 2 \}$
C) $\{ 2,4,6 , \ldots , 34 \}$
D) $\{ 34 \}$

Accepted Answer

The sample space for picking one even-numbered ball from a set of balls numbered 1 through 35 includes all the even numbers within that range, which are 2, 4, 6, ..., up to 34.

Question 14

Solve the problem.
-What are the odds in favor of drawing a 3 from these cards?

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

Accepted Answer

The answer of Solve the problem.
-What are the odds in...

Question 15

Solve the problem.
-What are the odds in favor of spinning a D on this spinner?

A) 5 to 1
B) 1 to 6
C) 1 to 7
D) 6 to 1

Accepted Answer

The answer of Solve the problem.
-What are the odds in...

Question 16

Solve the problem.
-What are the odds in favor of drawing an even number from these cards?

142454
A) 2 to 5
B) 5 to 2
C) 2 to 3
D) 3 to 2

Accepted Answer

The answer of Solve the problem.
-What are the odds in...

Question 17

List the elements in the sample space of the experiment.
-A box contains 10 red cards numbered 1 through 10 . List the sample space of picking one card from the box.
A) None of these
B) $\{ 1,2,3,4,5,6,7,8,9,10 \}$
C) $\{ 10 \}$
D) $\{ 100 \}$

Accepted Answer

The sample space of picking one card from a box containing 10 red cards numbered 1 through 10 is the set of all possible outcomes, which are the numbers 1 through 10.

Question 18

Find the probability.
-A bag contains 5 red marbles, 2 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?
A) $\frac { 4 } { 3 }$

B) $\frac { 1 } { 4 }$

C) $\frac { 3 } { 4 }$

D) 6

Accepted Answer

The total number of marbles is 8 (5 red + 2 blue + 1 green). The probability of not choosing a blue marble is the number of non-blue marbles (6) divided by the total number of marbles (8), which simplifies to $\frac{6}{8} = \frac{3}{4}$.

Question 19

Solve the problem.
-Cal is packing his suitcase to go on a trip. He wants to pack 3 pairs of pants chosen from the 8 pairs of pants in his closet and 4 shirts chosen from the 10 shirts in his closet. In how many ways can this
Be done?
A) 70,560
B) 1,693,440
C) 11,760
D) 282,240

Accepted Answer

To find the total number of ways Cal can pack his suitcase, we calculate the combinations separately for pants and shirts and then multiply the results. For pants, he chooses 3 out of 8, which is calculated using combinations as 8C3 = 8! / (3!(8-3)!) = 56 ways. For shirts, he chooses 4 out of 10, calculated as 10C4 = 10! / (4!(10-4)!) = 210 ways. Multiplying these gives 56 * 210 = 11,760 ways.

Question 20

List the elements in the sample space of the experiment.
-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) {36}
B) {1, 2, 3, 4, 5, 6}
C) None of these
D) {6}

Accepted Answer

The sample space of rolling a 6-sided die includes all the possible outcomes, which are the numbers 1, 2, 3, 4, 5, and 6.

Quiz 12: Further Topics in Algebra

Find the probability. -A 6-sided die is rolled. What is the probability of rolling a number less than $6 ?$

List the elements in the sample space of the experiment. -A group of 13 people are assigned numbers 1 through 13 . List the sample space of the event choosing a person with a number 5 or less.

Find the probability. -Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 5 ?

List the elements in the sample space of the experiment. -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.

List the elements in the sample space of the experiment. -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 .

Solve the problem. -What are the odds in favor of spinning an A on this spinner?

List the elements in the sample space of the experiment. -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.

Find the probability. -A bag contains 13 balls numbered 1 through 13 . What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

Find the probability. -A bag contains 3 red marbles, 2 blue marbles, and 8 green marbles. What is the probability of choosing a blue marble when one marble is drawn?

List the elements in the sample space of the experiment. -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.

Find the probability. -A lottery game contains 22 balls numbered 1 through 22 . What is the probability of choosing a ball numbered 23?

Find the probability. -Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10 ?

List the elements in the sample space of the experiment. -A lottery uses balls numbered 1 through 35 . List the sample space of the event picking one even-numbered ball.

Solve the problem. -What are the odds in favor of drawing a 3 from these cards?

Solve the problem. -What are the odds in favor of spinning a D on this spinner?

Solve the problem. -What are the odds in favor of drawing an even number from these cards? 142454

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

Find the probability. -A bag contains 5 red marbles, 2 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?

Solve the problem. -Cal is packing his suitcase to go on a trip. He wants to pack 3 pairs of pants chosen from the 8 pairs of pants in his closet and 4 shirts chosen from the 10 shirts in his closet. In how many ways can this Be done?

List the elements in the sample space of the experiment. -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.

Quiz 12: Further Topics in Algebra

Find the probability. -A 6-sided die is rolled. What is the probability of rolling a number less than 6?6 ?6?

List the elements in the sample space of the experiment. -A group of 13 people are assigned numbers 1 through 13 . List the sample space of the event choosing a person with a number 5 or less.

Find the probability. -Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 5 ?

List the elements in the sample space of the experiment. -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.

List the elements in the sample space of the experiment. -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 .

Solve the problem. -What are the odds in favor of spinning an A on this spinner?

List the elements in the sample space of the experiment. -An 8-sided die is rolled. The sides contain the numbers 1,2,3,4,5,6,7,81,2,3,4,5,6,7,81,2,3,4,5,6,7,8 . List the sample space of rolling one die.

Find the probability. -A bag contains 13 balls numbered 1 through 13 . What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

Find the probability. -A bag contains 3 red marbles, 2 blue marbles, and 8 green marbles. What is the probability of choosing a blue marble when one marble is drawn?

List the elements in the sample space of the experiment. -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.

Find the probability. -A lottery game contains 22 balls numbered 1 through 22 . What is the probability of choosing a ball numbered 23?

Find the probability. -Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10 ?

List the elements in the sample space of the experiment. -A lottery uses balls numbered 1 through 35 . List the sample space of the event picking one even-numbered ball.

Solve the problem. -What are the odds in favor of drawing a 3 from these cards?

Solve the problem. -What are the odds in favor of spinning a D on this spinner?

Solve the problem. -What are the odds in favor of drawing an even number from these cards? 142454

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

Find the probability. -A bag contains 5 red marbles, 2 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?

Solve the problem. -Cal is packing his suitcase to go on a trip. He wants to pack 3 pairs of pants chosen from the 8 pairs of pants in his closet and 4 shirts chosen from the 10 shirts in his closet. In how many ways can this Be done?

List the elements in the sample space of the experiment. -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.

Find the probability. -A 6-sided die is rolled. What is the probability of rolling a number less than $6 ?$

List the elements in the sample space of the experiment. -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.