Multiple Choice
A bag contains 6 red marbles, 3 white marbles, and 7 blue marbles. You pick a marble without looking. Find the probability of drawing a white marble.
A. three over eight
B. seven over sixteen
C. three over sixteen
D. thirteen over sixteen
The total number of marbles is 6 + 3 + 7 = 16. The probability of drawing a white marble is the number of white marbles (3) divided by the total number of marbles (16): 3/16. Therefore, the answer is C. three over sixteen.
A standard number cube with the numbers 1 through 6 is rolled. Find the probability of rolling a number less than 3. Find the probability of not rolling a number less than 3.
A. start fraction 1 over 3 end fraction; start fraction 2 over 3 end fraction
B. one-half; one-half
C. start fraction 5 over 6 end fraction ; one-half
D. start fraction 1 over 6 end fraction ; start fraction 5 over 6 end fraction
The numbers less than 3 on a standard number cube are 1 and 2. Therefore, the probability of rolling a number less than 3 is 2 out of 6 or 2/6, which can be simplified to 1/3. The probability of not rolling a number less than 3 is the probability of rolling a 3, 4, 5, or 6, which is 4 out of 6 or 4/6, which can be simplified to 2/3. Therefore, the answer is A. start fraction 1 over 3 end fraction; start fraction 2 over 3 end fraction.
A number cube is rolled 360 times and the results are recorded as follows: 54 ones, 60 twos, 66 threes, 71 fours, 35 fives, and 74 sixes. What is the experimental probability of rolling a two or a three?
A. 0.15
B. 0.1
C. 0.35
D. 0.65
The experimental probability of rolling a two or a three is the number of times a two or three was rolled divided by the total number of rolls: (60 + 66)/360 = 126/360 = 7/20. This can be simplified to 0.35, so the answer is C. 0.35.
Question 4 of 10
From a barrel of colored marbles, you randomly select 3 blue, 2 yellow, 7 red, 8 green, and 2 purple marbles. Find the experimental probability of randomly selecting either a green or a purple marble.
A. Start Fraction 9 over 22 End Fraction
B. start fraction 5 over 11 end fraction
C. The term shows 6 over 11.
D. one-half
The total number of marbles is 3 + 2 + 7 + 8 + 2 = 22. The number of green or purple marbles is 8 + 2 = 10. Therefore, the experimental probability of randomly selecting either a green or a purple marble is 10/22, which can be simplified to 5/11. Therefore, the answer is B. start fraction 5 over 11 end fraction.
A standard number cube is rolled 180 times. Predict how many times a 3 or a 5 will be the result.
A. 31 times
B. 60 times
C. 57 times
D. 30 times
When rolling a standard number cube, the probability of rolling a 3 or a 5 is 2/6 or 1/3. To predict how many times a 3 or a 5 will be the result in 180 rolls, we can multiply the probability by the total number of rolls: 1/3 x 180 = 60. Therefore, the answer is B. 60 times.
A new movie opened the other day. So far, 500,000 people have seen it. The producers of the movie needed to know if the people liked it. A random sample of 8,000 people were asked as they were leaving the theater if they liked the movie. Of those interviewed, 4,200 enjoyed the movie. Predict the total number of people who have enjoyed the movie.
A. 261,500 people
B. 262,645 people
C. 262,500 people
D. 263,000 people
If 4,200 people out of 8,000 enjoyed the movie, we can use this fraction to estimate the total number of people who enjoyed the movie out of the total number of people who have seen it:
4,200/8,000 = x/500,000
Solving for x, we get:
x = (4,200/8,000) x 500,000 = 262,500
Therefore, the answer is C. 262,500 people.
Jamestown Builders has a development of new homes. There are 6 different floor plans, 7 exterior colors, and an option of either a one-car or a two-car garage. How many choices are there for one home?
A. 84 choices
B. 126 choices
C. 15 choices
D. 42 choices
To determine the number of choices for one home, we need to multiply the number of options for each category together.
Number of floor plans = 6
Number of exterior colors = 7
Number of garage options = 2
Total number of choices = 6 x 7 x 2 = 84
Therefore, the answer is A. 84 choices.
If no digit may be used more than once, how many 5-digit numbers can be formed using only the digits 3, 8, 1, 2, 5, and 7?
A. 360 numbers
B. 717 numbers
C. 722 numbers
D. 720 numbers
The first digit of the 5-digit number can be any of the 6 digits. After that, the second digit can be any of the remaining 5 digits. This pattern continues until all 5 digits have been used. Therefore, the total number of possible 5-digit numbers is:
6 x 5 x 4 x 3 x 2 = 720
Therefore, the answer is D. 720 numbers.
A drawer contains 2 red socks, 3 white socks, and 3 blue socks. Without looking, you draw out a sock, return it, and draw out a second sock. What is the probability that the first sock is blue and the second sock is red?
A. three over eight
B. two over five
C. twenty-nine over thirty-two
D. three over thirty-two
The probability of drawing a blue sock on the first draw is 3/8. After replacing the sock and shuffling, the probability of drawing a red sock on the second draw is 2/8 (since there are now 2 red socks out of a total of 8 socks).
To find the probability of both events happening together (drawing a blue sock first and a red sock second), we multiply the probabilities:
(3/8) * (2/8) = 6/64 = 3/32
Therefore, the answer is D. three over thirty-two.
Two urns both contain green balls and red balls. Urn I contains 6 green balls and 4 red balls and Urn II contains 8 green balls and 7 red balls. A ball is drawn from each urn. What is the probability that both balls are red?
A. two over seventy-five
B. seven over fifty
C. seven over twenty-five
D. fourteen over seventy-five
The probability of drawing a red ball from Urn I is 4/10 or 2/5. The probability of drawing a red ball from Urn II is 7/15.
To find the probability of both events happening together (drawing a red ball from both urns), we multiply the probabilities:
(2/5) * (7/15) = 14/75
Therefore, the answer is D. fourteen over seventy-five.
Reflect on your experience in this course. You may want to think about specific concepts in math, or perhaps your habits for learning or studying math. Tell two ways you have experienced success so far. State two areas in which you can improve. Give details.
You may submit your response by typing in the box below or by using the record tool. Choose one method to submit your response.
Option A: Enter your response below.
As an AI language model, I do not have personal experiences. However, I can provide a sample response to the prompt:
Two ways I have experienced success in this course are staying organized and seeking help when needed. I have kept track of homework assignments and test dates in a planner, which has helped me manage my time and avoid procrastination. Additionally, I have not been afraid to approach my teacher for help when I struggled with a particular concept, which has helped me gain a deeper understanding of the material.
Two areas in which I can improve are practicing more problems and being more confident in my abilities. Instead of relying solely on examples shown in class, I should practice more problems to reinforce my understanding of the material. I also need to work on believing in myself when attempting more challenging problems. Sometimes, I doubt my abilities and get discouraged, which hinders my progress. By building confidence and persistence, I can overcome these obstacles and continue to succeed in math.