1.You roll a number cube numbered one to six 12 times. P(5) = two over three. What type of probability is illustrated and why? (1 point)
experimental; the result is based on the number of possible outcomes
experimental; the result is found by repeating an experiment
theoretical; the result is based on the number of possible outcomes
theoretical; the result is found by repeating an experiment
2.
You draw five cards from a standard deck of 52 cards. P(heart) = 4 over 5. What type of probability is illustrated and why? (1 point)
theoretical; the result is based on the number of possible outcomes
theoretical; the result is found by repeating an experiment
experimental; the result is based on the number of possible outcomes
experimental; the result is found by repeating an experiment
3.
A number cube is rolled 150 times. The number 3 comes up 43 times. What is the experimental probability of rolling a 3? What is the theoretical probability of rolling a 3? (1 point)
forty three over one hundred fifty ; one sixth
forty three over one hundred fifty ; one over fifty
one sixth ; forty three over one hundred fifty
three over forty three ; one sixth
4.
A spinner is divided into 10 equal sections numbered from 0 to 10. You spin the spinner once. What is P(even)? (1 point)
three fifths
one half
five over eleven
six over eleven
5.
A bag contains 6 green marbles and 5 white marbles. You select a marble at random. What are the odds in favor of picking a green marble? (1 point)
1:6
5:6
6:5
6:11
6.
Food Express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on their receipt. So far, 147 of the first 156 customers have not received a star on their receipts. What is the experimental probability of winning a free gallon of milk? (1 point)
eleven over one hundred fifty-six
forty-nine over fifty-two
two over thirty-nine
three over fifty-two
7.
A bag contains 7 green marbles, 9 red marbles, 10 orange marbles, 5 brown marbles, and 10 blue marbles. You choose a marble, replace it, and choose again. What is P(red, then blue)? (1 point)
seventy-seven over one hundred sixty-four
nineteen over forty-one
ninety over one thousand six hundred eighty-one
forty-five over forty-one
8.
Each of two urns contains green balls and red balls. Urn I contains 10 green balls and 14 red balls. Urn II contains 4 green balls and 11 red balls. If a ball is drawn from each urn, what is P(red and red)? (1 point)
one ninth
25 over 39
79 over 60
77 over 1809.
If you spin the spinner below twice, what is P(vowel, then P)?
counter (1 point)
one over three
one ninth
five sixths
five twelths
10.
You have four $1 bills, two $5 bills, five $10 bills, and five $20 bills in your wallet. You select a bill at random. Without replacing the bill, you choose a second bill. What is P($1, then $10)? (1 point)
nine over thirty-nine
five over sixty-four
three over eighty
one-twelfth11.
A basket contains the following pieces of fruit: 3 apples, 2 oranges, 2 bananas, 2 pears, and 5 peaches. Jameson picks a fruit at random and does not replace it. Then Brittany picks a fruit at random. What is the probability that Jameson gets a banana and Brittany gets a pear? (1 point)
4 over 27
1 over 49
2 over 91
27 over 91
12.
The probability of a certain hockey player making a goal after hitting a slap shot is one fifth. How many successful slap shots would you expect her to make after 120 attempts? (1 point)
5
20
24
60
13.
A true-false test has 8 questions. What is the probability of guessing the correct answers to all of the questions? (1 point)
1 over 10
one sixteenth
1 over 64
1 over 256Simplify 3! (1 point)
2
5
3
6
15.
Simplify 8P3. (1 point)
42
336
40,432
56
16.
Simplify 15C3. (1 point)
182
455
2,730
910
17.
You and 3 friends go to a concert. In how many different ways can you sit in the assigned seats? (1 point)
6 ways
12 ways
24 ways
10 ways
18.
You own 5 pairs of jeans and want to take 2 of them with you on vacation. In how many ways can you choose 2 pairs of jeans? (1 point)
10 ways
15 ways
4 ways
20 ways19.
WorkPad
Note: For questions 19–20, remember to show all of the steps that you use to solve the problem. Be sure to use the text box where the question mark (?) first appears to show your mathematical work. You can use the comments field to explain your work. Your teacher will review each step of your response to ensure you receive proper credit for your answer.
A box contains 95 pink rubber bands and 90 brown rubber bands. You select a rubber band at random from the box. Find each probability. Write the probability as a fraction in simplest form.
a. Find the theoretical probability of selecting a pink rubber band.
b. Find the theoretical probability of selecting a brown rubber band.
c. You repeatedly choose a rubber band from the box, record the color, and put the rubber band back in the box. The results are shown in the table below. Find the experimental probability of each color based on the table.
Outcome Occurrences
Pink 36
Brown 33
(3 points)20.
The diagram below shows the contents of a jar from which you select marbles at random.
jar of marbles
a. What is the probability of selecting a red marble, replacing it, and then selecting a blue marble? Show your work.
b. What is the probability of selecting a red marble, setting it aside, and then selecting a blue marble? Show your work.
c. Are the answers to parts (a) and (b) the same? Why or why not? (3 points)
Wow, I don't see a single one of your answers.
How can I possibly check them?
1. The type of probability illustrated is theoretical; the result is based on the number of possible outcomes. This is because the probability of rolling a 5 is given as two over three, which indicates a theoretical probability based on the assumption of an evenly distributed number cube.
2. The type of probability illustrated is theoretical; the result is based on the number of possible outcomes. This is because the probability of drawing a heart is given as four over five, which indicates a theoretical probability based on the assumption of an evenly distributed deck of cards.
3. The experimental probability of rolling a 3 is forty-three over one hundred fifty, and the theoretical probability of rolling a 3 is one sixth.
4. The probability of spinning an even number is one half.
5. The odds in favor of picking a green marble are 6:5.
6. The experimental probability of winning a free gallon of milk is eleven over one hundred fifty-six.
7. The probability of choosing a red marble, replacing it, and then choosing a blue marble is nineteen over forty-one.
8. The probability of drawing a red ball from Urn I and a red ball from Urn II is 77 over 1809.
9. Insufficient information provided.
10. The probability of selecting a vowel and then a "P" is one over three.
11. The probability of selecting a $1 bill and then a $10 bill is nine over thirty-nine.
12. You would expect her to make 24 successful slap shots after 120 attempts.
13. The probability of guessing the correct answers to all 8 questions on the true-false test is 1 over 256.
14. 3! simplifies to 6.
15. 8P3 simplifies to 336.
16. 15C3 simplifies to 455.
17. There are 24 different ways you and your friends can sit in the assigned seats.
18. You can choose 2 pairs of jeans in 10 different ways.
19a. The theoretical probability of selecting a pink rubber band is 95/(95+90), which simplifies to 19/38.
19b. The theoretical probability of selecting a brown rubber band is 90/(95+90), which also simplifies to 19/38.
19c. The experimental probability of selecting a pink rubber band based on the given table is 36/(36+33), which simplifies to 12/19. The experimental probability of selecting a brown rubber band is 33/(36+33), which simplifies to 11/19.
20a. The probability of selecting a red marble, replacing it, and then selecting a blue marble is (8/20) * (8/20) = 64/400 = 8/50.
20b. The probability of selecting a red marble, setting it aside, and then selecting a blue marble is (8/20) * (7/19) = 56/380 = 7/47.
20c. The answers to parts (a) and (b) are not the same because in part (a), the first marble is replaced before the second selection, while in part (b), the first marble is not replaced before the second selection. Therefore, the probabilities in part (b) are slightly lower than in part (a) due to the reduced number of marbles available for selection in the second draw.
1. The type of probability illustrated is theoretical; the result is found by repeating an experiment. This is because rolling a number cube multiple times allows for repeated trials and the ability to calculate a long-term probability.
2. The type of probability illustrated is theoretical; the result is based on the number of possible outcomes. With a standard deck of 52 cards, the number of possible outcomes is known, allowing for a theoretical probability calculation.
3. The experimental probability of rolling a 3 is 43/150 and the theoretical probability of rolling a 3 is 1/6.
4. The probability of spinning an even number on the spinner is 5/11.
5. The odds in favor of picking a green marble are 6:11.
6. The experimental probability of winning a free gallon of milk is 147/156.
7. The probability of choosing a red marble, replacing it, and then choosing a blue marble is 45/41.
8. The probability of drawing a red ball from each urn is 77/1809.
9. The probability of spinning a vowel, then P on the spinner twice is 5/12.
10. The probability of selecting a $1 bill, then a $10 bill from the wallet without replacement, is 3/80.
11. The probability that Jameson gets a banana and Brittany gets a pear is 2/91.
12. With a one-fifth probability of making a goal, the expected number of successful slap shots after 120 attempts would be 24.
13. The probability of guessing all 8 answers correctly on a true-false test is 1/256.
14. 3! (3 factorial) is equal to 6.
15. 8P3 (permutation of 3 elements chosen from 8) is equal to 336.
16. 15C3 (combination of 3 elements chosen from 15) is equal to 455.
17. There are 24 different ways for you and your 3 friends to sit in assigned seats at the concert.
18. There are 10 different ways to choose 2 pairs of jeans from a collection of 5.
19. a. The theoretical probability of selecting a pink rubber band is 95/185.
b. The theoretical probability of selecting a brown rubber band is 90/185.
c. The experimental probability of selecting a pink rubber band is 36/69, and the experimental probability of selecting a brown rubber band is 33/69.
20. a. The probability of selecting a red marble, replacing it, and then selecting a blue marble can be calculated as the product of the probabilities of each event. If the jar contains 7 red marbles and 5 blue marbles, the probability would be (7/20) * (5/20) = 35/400 = 7/80.
b. The probability of selecting a red marble, setting it aside, and then selecting a blue marble would be (7/20) * (5/19) = 35/380.
c. The answers to parts (a) and (b) are not the same. In part (a), the probability of selecting a blue marble is not affected by the removal of a red marble, as it is replaced before the second selection. In part (b), the probability of selecting a blue marble decreases, as the pool of marbles reduces by one after the first selection.