There are two numbers greater than 3 on a standard number cube: 4 and 5. The total number of possible outcomes is 6 (since there are 6 faces on a cube). Therefore, the probability of getting a number greater than 3 is 2 out of 6, which simplifies to 1/3.
The answer is B. one-third.
A single, standard number cube is tossed. What is the probability of getting a number greater than 3?
A. two-thirds
B. one-third
C. start fraction 1 over 6 end fraction
D. one-half
39 answers
A game involves spinning this spinner. What is the probability of the pointer landing on Y?
A circle is divided equally into eight sections.· Two of the sections are labeled with an upper B.
· One of the sections is labeled with an upper G.
· One of the sections is labeled with an upper Y.
· Four of the sections are labeled with an upper R.
· An arrow originating from the center of the circle is pointing at one of the sections with an upper R.
A. one-eighth
B. one-half
C. start fraction 5 over 8 end fraction
D. two-eighths
A circle is divided equally into eight sections.· Two of the sections are labeled with an upper B.
· One of the sections is labeled with an upper G.
· One of the sections is labeled with an upper Y.
· Four of the sections are labeled with an upper R.
· An arrow originating from the center of the circle is pointing at one of the sections with an upper R.
A. one-eighth
B. one-half
C. start fraction 5 over 8 end fraction
D. two-eighths
Since there is only one section labeled Y and there are a total of eight sections, the probability of landing on Y is 1/8.
The answer is A. one-eighth.
The answer is A. one-eighth.
The table shows the snack preferences of 50 shoppers at the mall. What is the probability that one shopper, selected at random from the 50 surveyed, preferred the potato chips or pretzels?
Food Survey
Food Number of Shoppers
Fruit snacks 9
Potato chips 12
Apple 3
Pretzels 14
Water 12
A. one over five
B. thirteen over twenty-five
C. one over ten
D. eighteen over twenty five
3 / 15
Food Survey
Food Number of Shoppers
Fruit snacks 9
Potato chips 12
Apple 3
Pretzels 14
Water 12
A. one over five
B. thirteen over twenty-five
C. one over ten
D. eighteen over twenty five
3 / 15
To find the probability of a shopper preferring potato chips or pretzels, we need to add the number of shoppers who preferred potato chips to the number of shoppers who preferred pretzels and divide by the total number of shoppers.
12 + 14 = 26 shoppers preferred either potato chips or pretzels.
The total number of shoppers is 50.
So, the probability of a shopper preferring potato chips or pretzels is 26/50, which simplifies to 13/25.
The answer is B. thirteen over twenty-five.
12 + 14 = 26 shoppers preferred either potato chips or pretzels.
The total number of shoppers is 50.
So, the probability of a shopper preferring potato chips or pretzels is 26/50, which simplifies to 13/25.
The answer is B. thirteen over twenty-five.
A standard number cube with the numbers 1 through 6 is rolled. Find the probability of rolling a number greater than 5.
A. start fraction 1 over 6 end fraction
B. one-third
C. one-fourth
D. two-thirds
A. start fraction 1 over 6 end fraction
B. one-third
C. one-fourth
D. two-thirds
There is only one number on the cube that is greater than 5, which is 6.
The total number of possible outcomes is 6 (since there are 6 faces on a cube).
Therefore, the probability of rolling a number greater than 5 is 1 out of 6, which simplifies to 1/6.
The answer is A. start fraction 1 over 6 end fraction.
The total number of possible outcomes is 6 (since there are 6 faces on a cube).
Therefore, the probability of rolling a number greater than 5 is 1 out of 6, which simplifies to 1/6.
The answer is A. start fraction 1 over 6 end fraction.
A number cube is rolled 360 times, and the results are recorded as follows: 96 ones, 31 twos, 49 threes, 76 fours, 45 fives, and 63 sixes. What is the experimental probability of rolling a 2 or a 3?
A. 0.16
B. 0.22
C. 0.37
D. 0.78
A. 0.16
B. 0.22
C. 0.37
D. 0.78
To find the experimental probability of rolling a 2 or a 3, we need to add the number of times a 2 or 3 was rolled (31 + 49 = 80) and divide by the total number of rolls (360).
So, the experimental probability of rolling a 2 or 3 is 80/360, which simplifies to 2/9 or approximately 0.22.
The answer is B. 0.22.
So, the experimental probability of rolling a 2 or 3 is 80/360, which simplifies to 2/9 or approximately 0.22.
The answer is B. 0.22.
From a barrel of colored marbles, you randomly select 4 blue, 5 yellow, 6 red, 2 green, and 5 purple marbles. Find the experimental probability of randomly selecting a marble that is not blue.
A. The term shows 6 over 13.
B. one-half
C. start fraction 9 over 11 end fraction
D. three-eighths
A. The term shows 6 over 13.
B. one-half
C. start fraction 9 over 11 end fraction
D. three-eighths
The total number of marbles is:
4 + 5 + 6 + 2 + 5 = 22
The number of marbles that are not blue is:
5 + 6 + 2 + 5 = 18
So, the experimental probability of randomly selecting a marble that is not blue is 18/22, which simplifies to 9/11.
The answer is C. start fraction 9 over 11 end fraction.
4 + 5 + 6 + 2 + 5 = 22
The number of marbles that are not blue is:
5 + 6 + 2 + 5 = 18
So, the experimental probability of randomly selecting a marble that is not blue is 18/22, which simplifies to 9/11.
The answer is C. start fraction 9 over 11 end fraction.
The probability of winning a game is 25%. How many times should you expect to win if you play 20 times?
A. 7 times
B. 10 times
C. 2 times
D. 5 times
A. 7 times
B. 10 times
C. 2 times
D. 5 times
If the probability of winning a game is 25%, then the probability of losing is 75%.
The expected number of wins out of 20 plays is equal to the total number of plays (20) multiplied by the probability of winning (25%), or:
20 x 0.25 = 5
So, you should expect to win 5 times if you play 20 times.
The answer is D. 5 times.
The expected number of wins out of 20 plays is equal to the total number of plays (20) multiplied by the probability of winning (25%), or:
20 x 0.25 = 5
So, you should expect to win 5 times if you play 20 times.
The answer is D. 5 times.
A survey showed that 36% of car owners prefer two-door cars, 52% prefer four-door cars, and 12% have no preference. You ask 300 people. How many do you think will prefer the two-door cars?
A. 108 people
B. 192 people
C. 253 people
D. 300 people
A. 108 people
B. 192 people
C. 253 people
D. 300 people
If 36% of car owners prefer two-door cars, and you are surveying 300 people, then you would expect:
0.36 x 300 = 108 people to prefer two-door cars.
So the answer is A. 108 people.
0.36 x 300 = 108 people to prefer two-door cars.
So the answer is A. 108 people.
Sally works in a factory that produces 1,000 televisions each day. When 40 televisions were sampled, it was found that 6 were defective. Estimate how many defective televisions are made each day.
A. 17 televisions
B. 96 televisions
C. 150 televisions
D. 360 televisions
A. 17 televisions
B. 96 televisions
C. 150 televisions
D. 360 televisions
To estimate how many defective televisions are made each day, we can set up a proportion using the sample data:
6/40 = x/1000
Solving for x, we get:
x = (6/40) x 1000 = 150
So, we can estimate that 150 defective televisions are made each day.
The answer is C. 150 televisions.
6/40 = x/1000
Solving for x, we get:
x = (6/40) x 1000 = 150
So, we can estimate that 150 defective televisions are made each day.
The answer is C. 150 televisions.
The spinner is divided into equal parts. Use a tree diagram to find the probability that the spinner will land on a consonant both times if the spinner is spun twice.
A circle is divided equally into three sections.· One of the sections is labeled with an upper E.
· One of the sections is labeled with an upper U.
· One of the sections is labeled with an upper N.
· An arrow originating from the center of the circle is pointing at the section labeled with upper U.
A. one-ninth
B. one-third
C. start fraction 5 over 9 end fraction
D. three-fourths
A circle is divided equally into three sections.· One of the sections is labeled with an upper E.
· One of the sections is labeled with an upper U.
· One of the sections is labeled with an upper N.
· An arrow originating from the center of the circle is pointing at the section labeled with upper U.
A. one-ninth
B. one-third
C. start fraction 5 over 9 end fraction
D. three-fourths
Since there are only 2 consonant sections (N and U) and 1 vowel section (E), the branch diagram would look like this:
```
C V
/ \ /
C V U
/ \ / |
N U E N
| |
N U
```
The probability of landing on a consonant on the first spin is 2/3. From there, there are two possible outcomes: either land on a consonant (probability 1/2) or land on a vowel (probability 1/2).
Therefore, the probability of landing on a consonant both times is:
(2/3) x (1/2) = 1/3
So, the answer is B. one-third.
```
C V
/ \ /
C V U
/ \ / |
N U E N
| |
N U
```
The probability of landing on a consonant on the first spin is 2/3. From there, there are two possible outcomes: either land on a consonant (probability 1/2) or land on a vowel (probability 1/2).
Therefore, the probability of landing on a consonant both times is:
(2/3) x (1/2) = 1/3
So, the answer is B. one-third.
An ice cream shop offers 5 different flavors of ice cream and 9 different toppings. How many choices are possible for a single serving of ice cream with one topping?
A. 14 choices
B. 45 choices
C. 52 choices
D. 63 choice
A. 14 choices
B. 45 choices
C. 52 choices
D. 63 choice
To determine how many choices are possible for a single serving of ice cream with one topping, we need to use the multiplication principle (also known as the counting principle), which states that if there are m ways to do one thing and n ways to do another thing, then there are m times n ways to do both things together.
In this case, there are 5 choices for the flavor of ice cream and 9 choices for the topping. So, using the multiplication principle, there are:
5 x 9 = 45 choices
So, the answer is B. 45 choices.
In this case, there are 5 choices for the flavor of ice cream and 9 choices for the topping. So, using the multiplication principle, there are:
5 x 9 = 45 choices
So, the answer is B. 45 choices.
Sammy likes to mix and match her 4 necklaces, 2 bracelets, and 3 hats. The colors are listed in the table. On Monday, she randomly picks a bracelet, a necklace, and a hat. What is the probability of Sammy choosing a red necklace and yellow bracelet?
Necklace Bracelet Hat
Red Red Silver
Green Yellow Yellow
Gold Green
Silver
A. one-half
B. one-fifth
C. one-ninth
D. one-eighth
Necklace Bracelet Hat
Red Red Silver
Green Yellow Yellow
Gold Green
Silver
A. one-half
B. one-fifth
C. one-ninth
D. one-eighth
The probability of Sammy choosing a red necklace and yellow bracelet can be found by multiplying the probabilities of each event, since the events are independent.
The probability of choosing a red necklace is 4 necklaces total, 1 of which is red, so the probability is 1/4.
The probability of choosing a yellow bracelet is 2 bracelets total, 1 of which is yellow, so the probability is 1/2.
Finally, the probability of choosing any hat does not matter, because it will not affect the probability of Sammy choosing a red necklace and yellow bracelet.
Multiplying the probabilities together, we get:
(1/4) x (1/2) = 1/8
So, the answer is D. one-eighth.
The probability of choosing a red necklace is 4 necklaces total, 1 of which is red, so the probability is 1/4.
The probability of choosing a yellow bracelet is 2 bracelets total, 1 of which is yellow, so the probability is 1/2.
Finally, the probability of choosing any hat does not matter, because it will not affect the probability of Sammy choosing a red necklace and yellow bracelet.
Multiplying the probabilities together, we get:
(1/4) x (1/2) = 1/8
So, the answer is D. one-eighth.
Which events are not independent?
A. You draw two colored marbles without replacement and get one red and one blue.
B. You pull a green tile from a bag of tiles, return it, and then pull a yellow tile.
C. You toss two coins and get one head, one tail.
D. You choose two different ice cream flavors for a cone.
A. You draw two colored marbles without replacement and get one red and one blue.
B. You pull a green tile from a bag of tiles, return it, and then pull a yellow tile.
C. You toss two coins and get one head, one tail.
D. You choose two different ice cream flavors for a cone.
A. You draw two colored marbles without replacement and get one red and one blue.
This event is not independent because the probability of drawing a blue marble on the second draw will depend on whether a blue marble was drawn on the first draw.
B. You pull a green tile from a bag of tiles, return it, and then pull a yellow tile.
This event is independent because the tile is returned to the bag after the first draw, so the probability of drawing a yellow tile on the second draw is not influenced by the first draw.
C. You toss two coins and get one head, one tail.
This event is not independent because the outcome of the second coin toss will depend on the outcome of the first coin toss. Specifically, if the first coin toss is a head, then the probability of the second coin toss being a tail is 1/2, while the probability of the second coin toss being a head is also 1/2.
D. You choose two different ice cream flavors for a cone.
This event is not independent because the probability of choosing a particular flavor for the second scoop will depend on which flavor was chosen for the first scoop. For example, if the first scoop is chocolate, then the probability of choosing vanilla for the second scoop will depend on how many vanilla scoops are left and how many total scoops are available.
Therefore, the answer is A and C.
This event is not independent because the probability of drawing a blue marble on the second draw will depend on whether a blue marble was drawn on the first draw.
B. You pull a green tile from a bag of tiles, return it, and then pull a yellow tile.
This event is independent because the tile is returned to the bag after the first draw, so the probability of drawing a yellow tile on the second draw is not influenced by the first draw.
C. You toss two coins and get one head, one tail.
This event is not independent because the outcome of the second coin toss will depend on the outcome of the first coin toss. Specifically, if the first coin toss is a head, then the probability of the second coin toss being a tail is 1/2, while the probability of the second coin toss being a head is also 1/2.
D. You choose two different ice cream flavors for a cone.
This event is not independent because the probability of choosing a particular flavor for the second scoop will depend on which flavor was chosen for the first scoop. For example, if the first scoop is chocolate, then the probability of choosing vanilla for the second scoop will depend on how many vanilla scoops are left and how many total scoops are available.
Therefore, the answer is A and C.
Which events are not independent?
A. You draw two colored marbles without replacement and get one red and one blue.
B. You pull a green tile from a bag of tiles, return it, and then pull a yellow tile.
C. You toss two coins and get one head, one tail.
D. You choose two different ice cream flavors for a cone.
only pick one
A. You draw two colored marbles without replacement and get one red and one blue.
B. You pull a green tile from a bag of tiles, return it, and then pull a yellow tile.
C. You toss two coins and get one head, one tail.
D. You choose two different ice cream flavors for a cone.
only pick one
A. You draw two colored marbles without replacement and get one red and one blue.
This event is not independent because the probability of drawing a blue marble on the second draw will depend on whether a blue marble was drawn on the first draw.
This event is not independent because the probability of drawing a blue marble on the second draw will depend on whether a blue marble was drawn on the first draw.
If a coin is tossed and a number cube is rolled, what is the probability that the coin shows heads and the number cube shows 3?
A. one-half
B. one-ninth
C. start fraction 1 over 6 end fraction
D. start fraction 1 over 12 end fraction
A. one-half
B. one-ninth
C. start fraction 1 over 6 end fraction
D. start fraction 1 over 12 end fraction
Assuming the coin is fair and balanced and the number cube is fair, the probability of the coin showing heads is 1/2, since there are two possible outcomes (heads or tails) and they are equally likely.
Similarly, the probability of the number cube showing 3 is 1/6, since there are six possible outcomes (the numbers 1 through 6) and they are equally likely.
To find the probability that both events occur (assuming they are independent), we multiply the probabilities:
(1/2) x (1/6) = 1/12
So, the answer is D. start fraction 1 over 12 end fraction.
Similarly, the probability of the number cube showing 3 is 1/6, since there are six possible outcomes (the numbers 1 through 6) and they are equally likely.
To find the probability that both events occur (assuming they are independent), we multiply the probabilities:
(1/2) x (1/6) = 1/12
So, the answer is D. start fraction 1 over 12 end fraction.
Short Answer
Note: Your teacher will grade your response to ensure you receive proper credit for your answer.
On Friday nights the local diner serves three main entrées, each with a choice of vegetable. The entrées are beef, chicken, and fish. The vegetables are spinach, broccoli, and carrots. How many possible dinners (entrée and vegetable combinations) does the diner serve? List them.
Note: Your teacher will grade your response to ensure you receive proper credit for your answer.
On Friday nights the local diner serves three main entrées, each with a choice of vegetable. The entrées are beef, chicken, and fish. The vegetables are spinach, broccoli, and carrots. How many possible dinners (entrée and vegetable combinations) does the diner serve? List them.
There are 9 possible dinner combinations that the diner serves:
1. Beef with spinach
2. Beef with broccoli
3. Beef with carrots
4. Chicken with spinach
5. Chicken with broccoli
6. Chicken with carrots
7. Fish with spinach
8. Fish with broccoli
9. Fish with carrots
1. Beef with spinach
2. Beef with broccoli
3. Beef with carrots
4. Chicken with spinach
5. Chicken with broccoli
6. Chicken with carrots
7. Fish with spinach
8. Fish with broccoli
9. Fish with carrots
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Marissa is researching information about martial arts students. She found that 7 out of 12 martial artists practice every day. There are 144 martial arts students at a school.
a. Predict how many students practice every day.
b. What is the sample size?
Marissa is researching information about martial arts students. She found that 7 out of 12 martial artists practice every day. There are 144 martial arts students at a school.
a. Predict how many students practice every day.
b. What is the sample size?
a. To predict how many students practice every day, we can set up a proportion using the information given:
7/12 = x/144
Solving for x, we get:
x = (7/12) x 144 = 84
So we can predict that 84 students practice every day.
b. The sample size is the total number of martial arts students at the school, which is given as 144.
Therefore, the sample size is 144.
7/12 = x/144
Solving for x, we get:
x = (7/12) x 144 = 84
So we can predict that 84 students practice every day.
b. The sample size is the total number of martial arts students at the school, which is given as 144.
Therefore, the sample size is 144.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form.
You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form.
The probability of rolling an even number on a number cube is 3/6 or 1/2, since there are three even numbers (2, 4, and 6) and six possible outcomes in total.
The probability of not rolling a 2 on the second roll is 5/6, since there are five possible outcomes (1, 3, 4, 5, and 6) that are not 2, and six possible outcomes in total (assuming the first roll was not a 2).
To find the probability of rolling an even number first and then not rolling a 2, we multiply the probabilities of each independent event:
P(even, then not 2) = (1/2) x (5/6) = 5/12
Therefore, the probability of rolling an even number first and then not rolling a 2 is 5/12.
The probability of not rolling a 2 on the second roll is 5/6, since there are five possible outcomes (1, 3, 4, 5, and 6) that are not 2, and six possible outcomes in total (assuming the first roll was not a 2).
To find the probability of rolling an even number first and then not rolling a 2, we multiply the probabilities of each independent event:
P(even, then not 2) = (1/2) x (5/6) = 5/12
Therefore, the probability of rolling an even number first and then not rolling a 2 is 5/12.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
a. The theoretical probability of rolling a 3 on a number cube is 1/6, since there is one 3 on the cube and six possible outcomes.
Therefore, the theoretical probability of rolling a 3 is 1/6.
b. The experimental probability of rolling a 3 is the number of times a 3 was rolled divided by the total number of rolls:
67/450
To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 1:
67/450
Therefore, the experimental probability of rolling a 3 is 67/450.
Therefore, the theoretical probability of rolling a 3 is 1/6.
b. The experimental probability of rolling a 3 is the number of times a 3 was rolled divided by the total number of rolls:
67/450
To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 1:
67/450
Therefore, the experimental probability of rolling a 3 is 67/450.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You mix the letters M, A, T, H, E, M, A, T, I, C, A, and L thoroughly. Without looking, you draw one letter. Find the probability P(A). Write the probability as:
a. a fraction in simplest form
b. a decimal
c. a percent
You mix the letters M, A, T, H, E, M, A, T, I, C, A, and L thoroughly. Without looking, you draw one letter. Find the probability P(A). Write the probability as:
a. a fraction in simplest form
b. a decimal
c. a percent
a. To find the probability of drawing an A, we need to determine how many A's are in the mix. Counting the letters, we see that there are 3 A's out of a total of 12 letters. So the probability of drawing an A is:
P(A) = 3/12
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 3, to get:
P(A) = 1/4
Therefore, the probability of drawing an A is 1/4.
b. To convert the fraction to a decimal, we divide the numerator by the denominator:
P(A) = 1
P(A) = 3/12
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 3, to get:
P(A) = 1/4
Therefore, the probability of drawing an A is 1/4.
b. To convert the fraction to a decimal, we divide the numerator by the denominator:
P(A) = 1
26 answers