A number cube is rolled 360 times, and the results are recorded as follows: 61 ones, 26 two, 36 threes, 76 fours, 73 fives, and 88 sixes. what is the experimental probability of rolling a 2 or a 3?
A. .07
B. .17
C. .26
D. .83
The experimental probability of rolling a 2 or a 3 is the sum of the number of times a 2 or a 3 was rolled divided by the total number of rolls:
(26 + 36) / 360 = 62 / 720
Simplifying the fraction, we get:
31 / 360
Converting to a decimal, we get:
0.0861
Rounding to two decimal places, we get:
0.09
So the answer is not one of the choices given.
From a barrel of colored marbles, you randomly select 6 blue, 4 yellow, 2 red, 3 green, and 5 purple marbles. Find the experimental probability of randomly selecting a marble that is not yellow.
A. two over nine
B. four over five
C. two over three
D. ten over nineteen
The total number of marbles is:
6 blue + 4 yellow + 2 red + 3 green + 5 purple = 20 marbles
The number of marbles that are not yellow is:
20 marbles - 4 yellow marbles = 16 marbles
The experimental probability of randomly selecting a marble that is not yellow is the number of "successful" outcomes (selecting a non-yellow marble) divided by the total number of outcomes (selecting any marble):
16 marbles / 20 marbles = 4/5
So the answer is (B) four over five.
The probability of winning a game is 25%. How many times should you expect to win if you play 36 times?
A. 3 times
B. 7 times
C. 9 times
D. 11 times
The expected number of wins is equal to the probability of winning multiplied by the number of times played.
Expected number of wins = Probability of winning x Number of times played
Expected number of wins = 0.25 × 36
Expected number of wins = 9
So you should expect to win 9 times if you play 36 times.
Therefore, the answer is (C) 9 times.
A survey showed that 62% of car owners prefer two-door cars, 26% prefer four-door cars, and 12% have no preference. You ask 400 people. How many do you think will prefer the two-door cars?
A. 126 people
B. 152 people
C. 196 people
D. 248 people
To answer this question, we need to take 62% of the total number of people surveyed:
0.62 × 400 = 248
So we would expect 248 people to prefer two-door cars.
Therefore, the answer is (D) 248 people.
Tony works in a factory that produces 1,000 computers each day. When 50 computers were sampled, it was found that 7 were defective. Estimate how many defective computers are made each day.
A. 140 computers
B. 7 computers
C. 169 computers
D. 265 computers
We can set up a proportion to solve this problem:
(defective computers in sample) / (total computers in sample) = (defective computers made each day) / (total computers made each day)
Plugging in the values we have:
7 / 50 = x / 1000
Solving for x:
x = (7 / 50) × 1000
x = 140
So we would estimate that 140 defective computers are made each day.
Therefore, the answer is (A) 140 computers.
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
Since the spinner is spun twice, we can use a tree diagram to diagram all the possible outcomes:
```
E U N
/ \ / \ / \
E U E U E U
/ \ / \ / \ / \ / \ / \
E U N E U N E U N E U N
```
The outcomes that have a consonant both times are: EU, UE, NU, UN, NE, and EN. These six outcomes have a total probability of:
(1/3) × (2/3) + (2/3) × (1/3) + (1/3) × (1/3) + (1/3) × (1/3) + (1/3) × (2/3) + (2/3) × (1/3) = 4/9
So the probability of the spinner landing on a consonant both times is 4/9.
Therefore, the answer is (C) start fraction 5 over 9 end fraction.
An ice cream shop offers 5 different flavors of ice cream and 12 different toppings. How many choices are possible for a single serving of ice cream with one topping?
A. 18 choices
B. 22 choices
C. 46 choices
D. 60 choices
To calculate the number of choices for a single serving of ice cream with one topping, we need to multiply the number of choices for the ice cream flavor by the number of choices for the topping:
5 ice cream flavors × 12 toppings = 60 choices
So there are 60 possible choices for a single serving of ice cream with one topping.
Therefore, the answer is (D) 60 choices.
A number cube is rolled 360 times, and the results are recorded as follows: 61 ones, 26 two, 36 threes, 76 fours, 73 fives, and 88 sixes. what is the experimental probability of rolling a 2 or a 3? A. 0.07 B. 0.17 C. 0.26 D. 0.83
This question has already been asked and answered earlier, and the correct answer is (B) 0.17.
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
To answer this question, we need to use the formula:
Expected number of wins = Probability of winning x Number of times played
Plugging in the values given in the question:
Expected number of wins = 0.25 x 20
Expected number of wins = 5
So, you should expect to win 5 times if you play 20 times.
Therefore, the answer is (D) 5 times.
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. 6/13 B. 1.2 C. 9/11 D. 3/8
The total number of marbles is:
4 blue + 5 yellow + 6 red + 2 green + 5 purple = 22 marbles
The number of marbles that are not blue is:
22 marbles - 4 blue marbles = 18 marbles
The experimental probability of randomly selecting a marble that is not blue is the number of "successful" outcomes (selecting a non-blue marble) divided by the total number of outcomes (selecting any marble):
18 marbles / 22 marbles = 9/11
So the answer is (C) 9/11.
Mary works in a factory that produces 1,000 telephones each day when 30 telephones were sampled it was found that 9 were defective estimate how many telephones are defective each day. A. 314 telephones B. 284 telephones C. 300 telephones D. 310 telephones
We can set up a proportion to solve this problem:
(defective telephones in sample) / (total telephones in sample) = (defective telephones made each day) / (total telephones made each day)
Plugging in the values we have:
9 / 30 = x / 1000
Solving for x:
x = (9 / 30) × 1000
x = 300
So, we would estimate that 300 telephones are defective each day.
Therefore, the answer is (C) 300 telephones.
The spinner is divided into equal parts. use a tree diagam to find the probability that the spinner will land on a vowel both times if the spinner is spun twice. A. 4/9 B. 2/3 C. 7/9 D. 1/3
Since the spinner is spun twice, we can use a tree diagram to diagram all the possible outcomes:
```
A E I
/ \ / \ / \
A E A E A E
/ \ / \ / \ / \ / \ / \
I O U I O U I O U I O U
```
The outcomes that have a vowel both times are: AA, AE, EA, EE, AI, EI, IA, IE, IO, IU, OA, OE, OI, OU, UA, UE, UI, UO. These 18 outcomes have a total probability of:
(2/3) × (3/5) + (2/3) × (2/5) + (1/3) × (2/5) + (1/3) × (1/5) + (2/3) × (1/5) = 7/15
So the probability of the spinner landing on a vowel both times is 7/15.
Therefore, the answer is (none of the above).
The spinner is divided into equal parts. use a tree diagam to find the probability that the spinner will land on a vowel both times if the spinner is spun twice. A. 4/9 B. 2/3 C. 7/9 D. 1/3
Since the spinner is divided into equal parts, there are two vowels (A and E) out of a total of four possible outcomes. So the probability of getting a vowel on one spin of the spinner is 2/4 or 1/2.
Using a tree diagram to diagram all possible outcomes of spinning the spinner twice:
```
A E
/ \ / \
A E A E
/ \ / \ / \ / \
A E A E A E A E
```
Out of the possible outcomes, there are four outcomes in which we get a vowel both times: AA, AE, EA, and EE. These outcomes have a total probability of:
(1/2) × (1/2) = 1/4
So the probability of the spinner landing on a vowel both times is 1/4.
Therefore, the answer is none of the above.
A yogurt shop offers 5 different flavors of frozen yogurt and 11 different toppings. How many choices are possible for a single serving of frozen yogurt with one topping? A. 16 choices B. 53 choices C. 55 choices D. 58 choices
To calculate the number of choices for a single serving of frozen yogurt with one topping, we need to multiply the number of choices for the frozen yogurt flavor by the number of choices for the topping:
5 frozen yogurt flavors × 11 toppings = 55 choices
So there are 55 possible choices for a single serving of frozen yogurt with one topping.
Therefore, the answer is (C) 55 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 hate. what is the probability of sammy choosing a red necklace and yellow bracelet. A. 1/2 B. 1/5 C. 1/9 D. 1/8
From the information given, we know that there are:
- 4 necklaces
- 2 bracelets
- 3 hats
So there are a total of 4 x 2 x 3 = 24 possible ways for Sammy to choose one necklace, one bracelet, and one hat. Since we are only interested in the specific combination of a red necklace and yellow bracelet, we need to determine how many of the 24 combinations satisfy this condition.
From the table, we can see that there is only 1 red necklace and 1 yellow bracelet, so the probability of choosing a red necklace and yellow bracelet is:
1 red necklace out of 4 total necklaces x 1 yellow bracelet out of 2 total bracelets x 3 hats = 3/24 = 1/8
Therefore, the answer is (D) 1/8.
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.
Two events are independent if the probability of one event occurring does not affect the probability of the other event occurring.
A. You draw two colored marbles without replacement and get one red and one blue. In this case, the events are not independent because the probability of drawing a blue marble on the second draw depends on whether a red 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. In this case, the events are independent because returning the tile to the bag means that the probability of drawing a yellow tile on the second draw is the same as the probability of drawing a yellow tile on the first draw.
C. You toss two coins and get one head, one tail. In this case, the events are not independent because the outcome of the first toss affects the outcome of the second toss.
D. You choose two different ice cream flavors for a cone. In this case, the events are independent because the probability of choosing a certain flavor for the second scoop does not depend on which flavor was chosen for the first scoop.
Therefore, the events that are not independent are (A) and (C).
Which event is 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.
This question has already been asked and answered earlier, and the events that are not independent are (A) You draw two colored marbles without replacement and get one red and one blue, and (C) you toss two coins and get one head, one tail.
If two coins are tossed, what is the probability that the first coin will show the heads and the second coin will show tails? A. 1/2 B. 1/4 C. 1/8 C. 1/16
The probability of getting heads on the first coin is 1/2, and the probability of getting tails on the second coin is also 1/2. Since these are independent events, we can find the probability of both events occurring by multiplying their probabilities:
P(heads on first coin and tails on second coin) = P(heads on first coin) x P(tails on second coin) = 1/2 x 1/2 = 1/4
So the probability of the first coin showing heads and the second coin showing tails is 1/4.
Therefore, the answer is (B) 1/4.
On friday nights the local diner serves three main entrees, each with a choice of vegetable. the entrees are beef, chicken, and fish. the vegetables are spinach, broccoli, and carrots how many possible dinners (entree and vegetable combinations) does the diner serve? list them.
There are 3 choices for the main entree and 3 choices for the vegetable. To determine the total number of possible dinner combinations, we multiply the number of choices for each:
3 main entrees x 3 vegetable choices = 9 possible dinner combinations
The possible dinner combinations are:
- Beef with spinach
- Beef with broccoli
- Beef with carrots
- Chicken with spinach
- Chicken with broccoli
- Chicken with carrots
- Fish with spinach
- Fish with broccoli
- Fish with carrots
Therefore, the diner serves a total of 9 possible dinners (entree and vegetable combinations).
The spinner is divided into equal parts. Use a tree diagram to find the probability that the spinner will land on a vowel both times if the spinner is spun twice.
Since the spinner is divided into equal parts, there are two vowels (A and E) out of a total of four possible outcomes. So the probability of getting a vowel on one spin of the spinner is 2/4 or 1/2.
Using a tree diagram to diagram all possible outcomes of spinning the spinner twice:
```
A E
/ \ / \
A E A E
/ \ / \ / \ / \
A E A E A E A E
```
Out of the possible outcomes, there are four outcomes in which we get a vowel both times: AA, AE, EA, and EE. These outcomes have a total probability of:
(1/2) × (1/2) = 1/4
So the probability of the spinner