Question 1

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.

Accepted Answer

The sample space of rolling a 6-sided die includes all the possible outcomes, which are the numbers 1 through 6.

Question 2

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?

Accepted Answer

The answer of Find the probability.
-Two 6-sided dice are rolled....

Question 3

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

Accepted Answer

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

Question 4

Solve the problem.
-How many ways can a class president, a class secretary, and a class treasurer be chosen from a group of 8 candidates?

Accepted Answer

The number of ways to choose a class president, a class secretary, and a class treasurer from a group of 8 candidates is a permutation problem because the order in which the positions are filled matters. The formula for permutations is P(n, r) = n! / (n-r)!, where n is the total number of items to choose from, r is the number of items to choose, and "!" denotes factorial, which is the product of all positive integers up to that number. Here, n = 8 (the total candidates) and r = 3 (the positions to be filled). Thus, P(8, 3) = 8! / (8-3)! = 8! / 5! = (8 * 7 * 6 * 5!) / 5! = 8 * 7 * 6 = 336.

Question 5

List the elements in the sample space of the experiment.
-A group of 19 people are assigned numbers 1 through 19. List the sample space of the event choosing a person with a number 5 or less.

Accepted Answer

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

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?

Accepted Answer

The probability of choosing a ball numbered 26 is 0 because there are no balls numbered 26 in a game that contains balls numbered 1 through 25.

Question 7

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

Accepted Answer

Numbers less than 6 on a 6-sided die are 1, 2, 3, 4, and 5, making 5 favorable outcomes out of 6 possible outcomes, so the probability is $\frac{5}{6}$.

Question 8

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.

Accepted Answer

The sample space consists of all possible pairs where the first element is a blue card (numbered 1 through 3) and the second element is a green card (numbered 1 through 4), resulting in 3*4=12 unique pairs.

Question 9

List the elements in the sample space of the experiment.
-A lottery uses balls numbered 1 through 31. List the sample space of the event picking one even-numbered ball.

Accepted Answer

The sample space for picking one even-numbered ball from a set numbered 1 through 31 includes all even numbers in that range, which are {2, 4, 6, ..., 30}.

Question 10

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.

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 6 possible outcomes: {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3)}.

Question 11

Find the probability.
-A bag contains 5 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?

Accepted Answer

The total number of marbles is 5 (red) + 3 (blue) + 1 (green) = 9. The number of marbles that are not blue is 5 (red) + 1 (green) = 6. Therefore, the probability of choosing a marble that is not blue is 6 out of 9, which simplifies to $\frac{2}{3}$.

Question 12

Find the probability.
-Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 3?

Accepted Answer

The sum of 3 can only be achieved by rolling a 1 on one die and a 2 on the other. Since there are 36 possible outcomes when rolling two dice (6 options for the first die multiplied by 6 options for the second die), and only 2 of these outcomes (1+2 and 2+1) sum to 3, the probability is $\frac{2}{36} = \frac{1}{18}$.

Question 13

Solve the problem.
-How many relay teams of 4 members can be chosen from a 7 member team to run in a relay race?

Accepted Answer

The answer of Solve the problem.
-How many relay teams of...

Question 14

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.

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 15

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?

Accepted Answer

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

Question 16

Solve the problem.
-Cal is packing his suitcase to go on a trip. He wants to pack 3 pairs of pants chosen from the 9 pairs of pants in his closet and 5 shirts chosen from the 10 shirts in his closet. In how many ways
Can this be done?

Accepted Answer

The number of ways to choose 3 pairs of pants from 9 is calculated using combinations: 9C3 = 9! / (3!(9-3)!) = 84 ways. The number of ways to choose 5 shirts from 10 is calculated using combinations: 10C5 = 10! / (5!(10-5)!) = 252 ways. To find the total number of ways to choose both pants and shirts, multiply the two: 84 * 252 = 21,168.

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.

Accepted Answer

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

Question 18

Solve the problem.
-A game involves choosing 6 numbers from the numbers 1 through 13. In how many ways can this be done?

Accepted Answer

This problem involves calculating combinations, as the order in which the numbers are chosen does not matter. The formula for combinations is C(n, r) = n! / [r!(n - r)!], where n is the total number of items to choose from, r is the number of items to choose, and "!" denotes factorial, the product of all positive integers up to that number. Here, n = 13 and r = 6, so the calculation is C(13, 6) = 13! / [6!(13 - 6)!] = 13! / (6!7!) = (13×12×11×10×9×8) / (6×5×4×3×2×1) = 1716.

Question 19

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

Accepted Answer

The answer of Find the probability.
-A bag contains 9 red...

Question 20

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.

Accepted Answer

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

Quiz 11: Further Topics in Algebra

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. -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?

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

Solve the problem. -How many ways can a class president, a class secretary, and a class treasurer be chosen from a group of 8 candidates?

List the elements in the sample space of the experiment. -A group of 19 people are assigned numbers 1 through 19. List the sample space of the event choosing a person with a number 5 or less.

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

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 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.

List the elements in the sample space of the experiment. -A lottery uses balls numbered 1 through 31. List the sample space of the event picking one even-numbered ball.

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.

Find the probability. -A bag contains 5 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. -Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 3?

Solve the problem. -How many relay teams of 4 members can be chosen from a 7 member team to run in a relay race?

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 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?

Solve the problem. -Cal is packing his suitcase to go on a trip. He wants to pack 3 pairs of pants chosen from the 9 pairs of pants in his closet and 5 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 box contains 10 red cards numbered 1 through 10. List the sample space of picking one card from the box.

Solve the problem. -A game involves choosing 6 numbers from the numbers 1 through 13. In how many ways can this be done?

Find the probability. -A bag contains 9 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. -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.