Question 1

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), (2, 1), (2, 2), (3, 1), (3, 2)}
C) {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3)}
D) {12}

Accepted Answer

The sample space consists of all possible outcomes of picking a blue card followed by a green card. Since there are 2 blue cards and 3 green cards, each blue card can be paired with any of the 3 green cards, resulting in 2*3 = 6 possible outcomes: {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3)}.

Question 2

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

Accepted Answer

The sample space for choosing a card with a number greater than 6 from a set of cards numbered 1 through 13 includes all numbers from 7 to 13, which matches option A.

Question 3

Find the probability.
-A 6-sided die is rolled. What is the probability of rolling a number less than 3? 
A) $\frac { 1 } { 3 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 1 } { 6 }$
D) $\frac { 2 } { 3 }$

Accepted Answer

Numbers less than 3 on a 6-sided die are 1 and 2, so there are 2 favorable outcomes out of 6 possible outcomes, giving a probability of $\frac{2}{6} = \frac{1}{3}$.

Question 4

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) $\frac { 1 } { 12 }$
B) $\frac { 5 } { 18 }$
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. There are 3 combinations to get these sums: (5,6), (6,5) for 11, and (6,6) for 12. Since there are 36 possible outcomes when rolling two dice (6 sides on the first die times 6 sides on the second die), the probability is $ \frac{3}{36} = \frac{1}{12} $.

Question 5

Find the probability.
-A bag contains 6 red marbles, 3 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) 7
B) $\frac { 3 } { 10 }$
C) $\frac { 10 } { 7 }$
D) $\frac { 7 } { 10 }$

Accepted Answer

The total number of marbles is 6 (red) + 3 (blue) + 1 (green) = 10. The number of marbles that are not blue is 6 (red) + 1 (green) = 7. Therefore, the probability of choosing a marble that is not blue is 7 out of 10, or $\frac{7}{10}$.

Question 6

Find the probability.
-A lottery game contains 25 balls numbered 1 through 25. What is the probability of choosing a ball numbered 26?
A) 25
B) 1
C) 251
D) 0

Accepted Answer

Since there are no balls numbered 26 in a set of balls numbered 1 through 25, the probability of choosing a ball numbered 26 is 0.

Question 7

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) {34}
B) {2}
C) {2, 4, 6, . . ., 34}
D) {1, 2, 3, . . ., 35}

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 8

A game involves choosing 4 numbers from the numbers 1 through 13. In how many ways can this be done?
A) 695
B) 715
C) 17,160
D) 723

Accepted Answer

The number of ways to choose 4 numbers out of 13 is calculated using the combination formula, which is C(n, k) = n! / [k!(n-k)!], where n is the total number of items, and k is the number of items to choose. Here, n=13 and k=4, so C(13, 4) = 13! / (4! * 9!) = (13*12*11*10) / (4*3*2*1) = 715.

Question 9

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

Accepted Answer

The answer of What are the odds in favor of...

Question 10

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

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 11

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

Accepted Answer

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

Question 12

Cal is packing his suitcase to go on a trip. He wants to pack 4 pairs of pants chosen from the 6 pairs of pants in his closet and 5 shirts chosen from the 8 shirts in his closet. In how many ways can this be done?
A) 20,160
B) 2,419,200
C) 840
D) 100,800

Accepted Answer

The number of ways to choose 4 pairs of pants from 6 is given by the combination formula C(6,4) = 15. The number of ways to choose 5 shirts from 8 is C(8,5) = 56. The total number of ways to choose both is 15 * 56 = 840.

Question 13

What are the odds in favor of spinning a D on this spinner? 
A) 5 to 1
B) 6 to 1
C) 1 to 6
D) 1 to 7

Accepted Answer

The answer of What are the odds in favor of...

Question 14

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) $\frac { 5 } { 6 }$
B) $\frac { 1 } { 9 }$
C) 4
D) $\frac { 8 } { 9 }$

Accepted Answer

The possible combinations to get a sum of 5 are (1,4), (2,3), (3,2), and (4,1), which are 4 out of the 36 possible outcomes (since each die has 6 sides, there are 6x6=36 total outcomes). Therefore, the probability is $\frac{4}{36} = \frac{1}{9}$.

Question 15

List the elements in the sample space of the experiment.
-A group of 18 people are assigned numbers 1 through 18. List the sample space of the event choosing a person with a number 5 or less.
A) {1, 2, 3, 4, 5}
B) {1, 2, 3, 4}
C) {18}
D) {1}

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 16

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

Accepted Answer

The sample space of rolling an 8-sided die includes all the possible outcomes, which are the numbers 1 through 8.

Question 17

Find the probability.
-A bag contains 8 red marbles, 2 blue marbles, and 5 green marbles. What is the probability of choosing a blue marble when one marble is drawn? 
A) $\frac { 8 } { 15 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 5 }$
D) $\frac { 2 } { 15 }$

Accepted Answer

The total number of marbles is 8 (red) + 2 (blue) + 5 (green) = 15. The probability of drawing a blue marble is the number of blue marbles (2) divided by the total number of marbles (15), which is $\frac{2}{15}$.

Question 18

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) {7}
C) {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (4, 3)}
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)}

Accepted Answer

The sample space consists of all possible ordered pairs where the first element is a blue card (1, 2, or 3) and the second element is a green card (1, 2, 3, or 4), resulting in 12 possible combinations.

Question 19

Find the probability.
-A bag contains 19 balls numbered 1 through 19. What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?
A) $\frac { 9 } { 19 }$
B) $\frac { 19 } { 9 }$
C) 9
D) $\frac { 2 } { 19 }$

Accepted Answer

There are 19 balls in total, with numbers from 1 to 19. Among these, the even numbers are 2, 4, 6, 8, 10, 12, 14, 16, and 18, making a total of 9 even-numbered balls. Therefore, the probability of drawing an even-numbered ball is $\frac{9}{19}$.

Question 20

How many relay teams of 4 members can be chosen from a 6 member team to run in a relay race?
A) 24
B) 360
C) 120
D) 18

Accepted Answer

The answer of How many relay teams of 4 members...

Quiz 7: Arithmetic Sequence: Common Difference and First n Terms

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.

Find the probability. -A 6-sided die is rolled. What is the probability of rolling a number less than 3?

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?

Find the probability. -A bag contains 6 red marbles, 3 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?

Find the probability. -A lottery game contains 25 balls numbered 1 through 25. What is the probability of choosing a ball numbered 26?

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 game involves choosing 4 numbers from the numbers 1 through 13. In how many ways can this be done?

What are the odds in favor of spinning an A on this spinner?

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.

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.

Cal is packing his suitcase to go on a trip. He wants to pack 4 pairs of pants chosen from the 6 pairs of pants in his closet and 5 shirts chosen from the 8 shirts in his closet. In how many ways can this be done?

What are the odds in favor of spinning a D on this spinner?

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 group of 18 people are assigned numbers 1 through 18. List the sample space of the event choosing a person with a number 5 or less.

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 8 red marbles, 2 blue marbles, and 5 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 bag contains 19 balls numbered 1 through 19. What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

How many relay teams of 4 members can be chosen from a 6 member team to run in a relay race?