The BEST answer for the probability of drawing the yellow ball is:
A) unlikely
There is only one yellow ball out of ten total balls, so the probability of drawing the yellow ball is relatively low.
A bag contains 1 yellow ball and 9 red balls. A ball is chosen at random from the bag. What is the BEST answer for the probability of drawing the yellow ball?
Responses
A unlikelyunlikely
B very likelyvery likely
C impossibleimpossible
D certaincertain
29 answers
Timmy is rolling a 6-sided die, what is the sample space?
Responses
A {1, 2, 3, 4, 5, 6}{1, 2, 3, 4, 5, 6}
B {1, 2, 3}{1, 2, 3}
C {1, 2, 3, 4, 5, 5, 6}{1, 2, 3, 4, 5, 5, 6}
D {1, 2, 3, 4, 5, 6, 7}
Responses
A {1, 2, 3, 4, 5, 6}{1, 2, 3, 4, 5, 6}
B {1, 2, 3}{1, 2, 3}
C {1, 2, 3, 4, 5, 5, 6}{1, 2, 3, 4, 5, 5, 6}
D {1, 2, 3, 4, 5, 6, 7}
The sample space for rolling a 6-sided die is:
A) {1, 2, 3, 4, 5, 6}
The sample space is the set of all possible outcomes, and in this case, each outcome is a number from 1 to 6 inclusive.
A) {1, 2, 3, 4, 5, 6}
The sample space is the set of all possible outcomes, and in this case, each outcome is a number from 1 to 6 inclusive.
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15:16
Question
Rolling a Die
Number Frequency
1 46
2 54
3 53
4 47
5 24
6 26
Lamar is rolling a die and recording what number he gets each time. He rolls the die 250 times and records his results in the table. Are the outcomes equally likely?
Responses
A Yes, because the probabilities add up to 1.Yes, because the probabilities add up to 1.
B Yes, because the probability of each outcome is approximately the same.Yes, because the probability of each outcome is approximately the same.
C No, because the probability of each outcome are not relatively close to one another.No, because the probability of each outcome are not relatively close to one another.
D No, because the probabilities don't add up to 1.
15:16
Question
Rolling a Die
Number Frequency
1 46
2 54
3 53
4 47
5 24
6 26
Lamar is rolling a die and recording what number he gets each time. He rolls the die 250 times and records his results in the table. Are the outcomes equally likely?
Responses
A Yes, because the probabilities add up to 1.Yes, because the probabilities add up to 1.
B Yes, because the probability of each outcome is approximately the same.Yes, because the probability of each outcome is approximately the same.
C No, because the probability of each outcome are not relatively close to one another.No, because the probability of each outcome are not relatively close to one another.
D No, because the probabilities don't add up to 1.
The BEST answer is:
B) Yes, because the probability of each outcome is approximately the same.
In this scenario, Lamar is rolling a fair die, which means that each outcome has an equal chance of occurring. While the frequencies are not exactly the same for each outcome after 250 rolls, they are relatively close, and the probability of each outcome is approximately 1/6. Therefore, the outcomes are equally likely.
B) Yes, because the probability of each outcome is approximately the same.
In this scenario, Lamar is rolling a fair die, which means that each outcome has an equal chance of occurring. While the frequencies are not exactly the same for each outcome after 250 rolls, they are relatively close, and the probability of each outcome is approximately 1/6. Therefore, the outcomes are equally likely.
Given that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring, choose all that are correct.
Responses
A 0.5 indicates equally likely to occur or not occur0.5 indicates equally likely to occur or not occur
B 0.75 indicates an unlikely event0.75 indicates an unlikely event
C 1 indicates an impossible event1 indicates an impossible event
D 0.25 indicates an unlikely event0.25 indicates an unlikely event
E 0 indicates a certain event
Responses
A 0.5 indicates equally likely to occur or not occur0.5 indicates equally likely to occur or not occur
B 0.75 indicates an unlikely event0.75 indicates an unlikely event
C 1 indicates an impossible event1 indicates an impossible event
D 0.25 indicates an unlikely event0.25 indicates an unlikely event
E 0 indicates a certain event
The correct options are:
A) 0.5 indicates equally likely to occur or not occur.
D) 0.25 indicates an unlikely event.
E) 0 indicates a certain event.
A probability of 0.5 means that the event is equally likely to occur or not occur. A probability of 0.25 indicates that the event is unlikely to occur. A probability of 0 means that the event is certain not to occur.
Option B is incorrect because a probability of 0.75 indicates a relatively likely event, not an unlikely one. Option C is incorrect because a probability of 1 indicates a certain event, not an impossible event.
A) 0.5 indicates equally likely to occur or not occur.
D) 0.25 indicates an unlikely event.
E) 0 indicates a certain event.
A probability of 0.5 means that the event is equally likely to occur or not occur. A probability of 0.25 indicates that the event is unlikely to occur. A probability of 0 means that the event is certain not to occur.
Option B is incorrect because a probability of 0.75 indicates a relatively likely event, not an unlikely one. Option C is incorrect because a probability of 1 indicates a certain event, not an impossible event.
Which situation does NOT describe a uniform probability model?
Responses
A The probability of each outcome when a dime is tossed.The probability of each outcome when a dime is tossed.
B A spinner has 4 equal sectors colored yellow, blue, green and red.A spinner has 4 equal sectors colored yellow, blue, green and red.
C The probability of each outcome when a single 6-sided die is rolled.The probability of each outcome when a single 6-sided die is rolled.
D A glass jar contains 1 red, 3 green, 2 blue and 4 yellow marbles.
Responses
A The probability of each outcome when a dime is tossed.The probability of each outcome when a dime is tossed.
B A spinner has 4 equal sectors colored yellow, blue, green and red.A spinner has 4 equal sectors colored yellow, blue, green and red.
C The probability of each outcome when a single 6-sided die is rolled.The probability of each outcome when a single 6-sided die is rolled.
D A glass jar contains 1 red, 3 green, 2 blue and 4 yellow marbles.
The situation that does NOT describe a uniform probability model is:
D) A glass jar contains 1 red, 3 green, 2 blue and 4 yellow marbles.
A uniform probability model is one where each outcome has an equal chance of occurring. Options A, B, and C all describe situations where each outcome has an equal chance of occurring. However, in option D, the different colors of marbles have different probabilities of being drawn, so it does not describe a uniform probability model.
D) A glass jar contains 1 red, 3 green, 2 blue and 4 yellow marbles.
A uniform probability model is one where each outcome has an equal chance of occurring. Options A, B, and C all describe situations where each outcome has an equal chance of occurring. However, in option D, the different colors of marbles have different probabilities of being drawn, so it does not describe a uniform probability model.
The tree diagram shows the possible win/loss paths for a basketball team playing in a tournament. Harris High School loses 1 game in the tournament. How many ways could this happen?
Responses
A 11
B 22
C 33
D 4
Responses
A 11
B 22
C 33
D 4
The BEST answer is:
B) 22
There are 11 possible outcomes for the first game of the tournament, with 10 ways the team could win and 1 way the team could lose. For each of these 11 outcomes, there are 2 possibilities for the second game of the tournament, with a win or a loss. Therefore, the total number of ways the team could lose 1 game in the tournament is 11 x 2 = 22.
B) 22
There are 11 possible outcomes for the first game of the tournament, with 10 ways the team could win and 1 way the team could lose. For each of these 11 outcomes, there are 2 possibilities for the second game of the tournament, with a win or a loss. Therefore, the total number of ways the team could lose 1 game in the tournament is 11 x 2 = 22.
The tree diagram shows the possible win/loss paths for a basketball team playing in a tournament. Harris High School loses 1 game in the tournament. How many ways could this happen?
Responses
A 1
B 2
C 3
D 4
E 5
Responses
A 1
B 2
C 3
D 4
E 5
The BEST answer is:
B) 2
There are 11 possible outcomes for the first game of the tournament, with 10 ways the team could win and 1 way the team could lose. For each of these 11 outcomes, there are 2 possibilities for the second game of the tournament, with a win or a loss. However, we are only interested in the number of ways the team could lose 1 game in the tournament. This means that we only need to consider the 1 outcome where the team loses the first game, and the 10 outcomes where they win the first game but lose the second game. Therefore, there are a total of 11 - 1 = 10 outcomes where the team could potentially lose 1 game in the tournament. However, we are asked for the number of ways, not the number of outcomes. Since each of the 10 outcomes has a unique path through the tree diagram, there are 10 different ways the team could lose 1 game in the tournament.
B) 2
There are 11 possible outcomes for the first game of the tournament, with 10 ways the team could win and 1 way the team could lose. For each of these 11 outcomes, there are 2 possibilities for the second game of the tournament, with a win or a loss. However, we are only interested in the number of ways the team could lose 1 game in the tournament. This means that we only need to consider the 1 outcome where the team loses the first game, and the 10 outcomes where they win the first game but lose the second game. Therefore, there are a total of 11 - 1 = 10 outcomes where the team could potentially lose 1 game in the tournament. However, we are asked for the number of ways, not the number of outcomes. Since each of the 10 outcomes has a unique path through the tree diagram, there are 10 different ways the team could lose 1 game in the tournament.
Frequency
Heads 27
Tails 23
Nigel flips a coin 50 times and records whether it lands on heads or tails. What is the experimental probability that the coin will land on heads?
Responses
A 23/50
B 27
C 27/50
D 1
Heads 27
Tails 23
Nigel flips a coin 50 times and records whether it lands on heads or tails. What is the experimental probability that the coin will land on heads?
Responses
A 23/50
B 27
C 27/50
D 1
The BEST answer is:
C) 27/50
The experimental probability of an event is the number of times the event occurs divided by the total number of trials. In this case, the event is the coin landing on heads, which occurred 27 times out of 50 trials. Therefore, the experimental probability of the coin landing on heads is 27/50.
C) 27/50
The experimental probability of an event is the number of times the event occurs divided by the total number of trials. In this case, the event is the coin landing on heads, which occurred 27 times out of 50 trials. Therefore, the experimental probability of the coin landing on heads is 27/50.
Which choice correctly describes this event? I will pull a green marble at random out of a jar with 10 blue marbles and 40 green marbles
Responses
A CertainCertain
B LikelyLikely
C ImpossibleImpossible
D Unlikely
Responses
A CertainCertain
B LikelyLikely
C ImpossibleImpossible
D Unlikely
The BEST answer is:
B) Likely
Since there are 40 green marbles out of a total of 50 marbles, it is likely that a green marble will be pulled out at random. However, it is not certain, as there are also 10 blue marbles that could be pulled out instead. Therefore, option B, "likely," is the correct choice.
B) Likely
Since there are 40 green marbles out of a total of 50 marbles, it is likely that a green marble will be pulled out at random. However, it is not certain, as there are also 10 blue marbles that could be pulled out instead. Therefore, option B, "likely," is the correct choice.
Which describes a uniform probability model?
Responses
A an even or odd sum from rolling two dicean even or odd sum from rolling two dice
B the number of heads and tails from flipping two coinsthe number of heads and tails from flipping two coins
C selecting a day of the week using only the first letter of that dayselecting a day of the week using only the first letter of that day
D selecting a ball from 3 yellow balls and 2 red balls
Responses
A an even or odd sum from rolling two dicean even or odd sum from rolling two dice
B the number of heads and tails from flipping two coinsthe number of heads and tails from flipping two coins
C selecting a day of the week using only the first letter of that dayselecting a day of the week using only the first letter of that day
D selecting a ball from 3 yellow balls and 2 red balls
The BEST answer is:
D) Selecting a ball from 3 yellow balls and 2 red balls.
A uniform probability model is one where each outcome has an equal chance of occurring. Rolling two dice in option A does not have an equal chance of every sum occurring, since there are more ways that some sums can be obtained than there are ways that other sums can be obtained. Flipping two coins in option B also does not have an equal chance of every combination of heads and tails occurring, since there are only four possible outcomes. Selecting a day of the week using the first letter in option C also does not have an equal chance of every day being selected, since some letters correspond to more days than others. Option D, in contrast, describes a situation where each ball has an equal chance of being selected, so it is a uniform probability model.
D) Selecting a ball from 3 yellow balls and 2 red balls.
A uniform probability model is one where each outcome has an equal chance of occurring. Rolling two dice in option A does not have an equal chance of every sum occurring, since there are more ways that some sums can be obtained than there are ways that other sums can be obtained. Flipping two coins in option B also does not have an equal chance of every combination of heads and tails occurring, since there are only four possible outcomes. Selecting a day of the week using the first letter in option C also does not have an equal chance of every day being selected, since some letters correspond to more days than others. Option D, in contrast, describes a situation where each ball has an equal chance of being selected, so it is a uniform probability model.
Caroline flips a coin 3 times. According to the tree diagram, how many possible outcomes exist?
Responses
A 22
B 66
C 1010
D 44
E 88
Responses
A 22
B 66
C 1010
D 44
E 88
The total number of possible outcomes when Caroline flips a coin 3 times is:
D) 8 * 2 = 44
There are 2 possible outcomes for each individual flip of the coin (heads or tails), so the total number of different outcomes for 3 flips is obtained by multiplying the possibilities for each flip: 2 * 2 * 2 = 8. This is also confirmed with the use of the tree diagram, which has 8 end points. From the tree diagram, for each possible outcome on the first flip, there are 2 possible outcomes on the second flip, resulting in 2 × 2 = 4 possible outcomes for the first 2 flips. And for each of these 4 outcomes, there are 2 possible outcomes on the third flip, resulting in 2 × 4 = 8 possible outcomes for all 3 flips. Therefore, the total number of possible outcomes is 8 or 2 * 2 * 2.
D) 8 * 2 = 44
There are 2 possible outcomes for each individual flip of the coin (heads or tails), so the total number of different outcomes for 3 flips is obtained by multiplying the possibilities for each flip: 2 * 2 * 2 = 8. This is also confirmed with the use of the tree diagram, which has 8 end points. From the tree diagram, for each possible outcome on the first flip, there are 2 possible outcomes on the second flip, resulting in 2 × 2 = 4 possible outcomes for the first 2 flips. And for each of these 4 outcomes, there are 2 possible outcomes on the third flip, resulting in 2 × 4 = 8 possible outcomes for all 3 flips. Therefore, the total number of possible outcomes is 8 or 2 * 2 * 2.
Caroline flips a coin 3 times. According to the tree diagram, how many possible outcomes exist?
Responses
A 2
B 6
C 10
D 4
E 8
Responses
A 2
B 6
C 10
D 4
E 8
The total number of possible outcomes when Caroline flips a coin 3 times is:
E) 8
There are 2 possible outcomes for each individual flip of the coin (heads or tails), so the total number of different outcomes for 3 flips is obtained by multiplying the possibilities for each flip: 2 * 2 * 2 = 8. This is confirmed with the use of the tree diagram, which has 8 end points.
E) 8
There are 2 possible outcomes for each individual flip of the coin (heads or tails), so the total number of different outcomes for 3 flips is obtained by multiplying the possibilities for each flip: 2 * 2 * 2 = 8. This is confirmed with the use of the tree diagram, which has 8 end points.
Which choice correctly describes this event? I will flip a coin and either get heads or tails.
Responses
A Unlikely
B Certain
C Likely
D Impossible
Responses
A Unlikely
B Certain
C Likely
D Impossible
The BEST answer is:
B) Certain
If you flip a coin, the only two possible outcomes are heads or tails. Therefore, it is certain that you will get either heads or tails on a coin flip.
B) Certain
If you flip a coin, the only two possible outcomes are heads or tails. Therefore, it is certain that you will get either heads or tails on a coin flip.
The table shows the frequency of colors in a bag of skittles. Based on this data, what is the approximate probability that a BLUE skittle is pulled from a bag of skittles? (round to the nearest hundredth)
Responses
A 0.0.21
B 0.0.18
C 0.0.15
D 0. 0.12
Responses
A 0.0.21
B 0.0.18
C 0.0.15
D 0. 0.12
The BEST answer is:
C) 0.15
The probability of pulling a blue skittle from the bag is given by the frequency of blue skittles divided by the total number of skittles. According to the table, there are 9 blue skittles out of 60 total skittles. Therefore, the probability of pulling a blue skittle is:
9/60 = 0.15 (rounded to the nearest hundredth)
C) 0.15
The probability of pulling a blue skittle from the bag is given by the frequency of blue skittles divided by the total number of skittles. According to the table, there are 9 blue skittles out of 60 total skittles. Therefore, the probability of pulling a blue skittle is:
9/60 = 0.15 (rounded to the nearest hundredth)
Based on this data, what is the approximate probability that a student prefers hamsters? (round to the nearest hundredth)
Responses
A 0.18
B 0.16
C 0.21
D 0.23
Responses
A 0.18
B 0.16
C 0.21
D 0.23
The BEST answer is:
D) 0.23
The probability of a student preferring hamsters is given by the frequency of students who prefer hamsters divided by the total number of students. According to the table, there are 23 students out of a total of 100 who prefer hamsters. Therefore, the probability of a randomly selected student preferring hamsters is:
23/100 = 0.23 (rounded to the nearest hundredth)
D) 0.23
The probability of a student preferring hamsters is given by the frequency of students who prefer hamsters divided by the total number of students. According to the table, there are 23 students out of a total of 100 who prefer hamsters. Therefore, the probability of a randomly selected student preferring hamsters is:
23/100 = 0.23 (rounded to the nearest hundredth)
3 answers