91586 – Worked Solutions - 2025
QUESTION THREE
3.14 (AS 91586) – 2025 Answers
Quite often, there are different ways to solve a Mathematics problem.
These solutions/strategies show one possible way to solve them.
Question 3 (a)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
Use a probability distribution model to estimate the probability of observing fewer than 3 harmful or inappropriate posts.
State the name and parameters of this distribution as part of your answer.
Question 3 (a)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
Use a probability distribution model to estimate the probability of observing fewer than 3 harmful or inappropriate posts.
State the name and parameters of this distribution as part of your answer.
Question 3 (a)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
Use a probability distribution model to estimate the probability of observing fewer than 3 harmful or inappropriate posts.
State the name and parameters of this distribution as part of your answer.
Question 3 (a)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
Use a probability distribution model to estimate the probability of observing fewer than 3 harmful or inappropriate posts.
State the name and parameters of this distribution as part of your answer.
This problem can be solved with the Binomial Distribution
Only two outcomes:
Harmful Content OR Not Harmful Content
Question 3 (a)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
Use a probability distribution model to estimate the probability of observing fewer than 3 harmful or inappropriate posts.
State the name and parameters of this distribution as part of your answer.
Question 3 (a)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
Use a probability distribution model to estimate the probability of observing fewer than 3 harmful or inappropriate posts.
State the name and parameters of this distribution as part of your answer.
Question 3 (a)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
Use a probability distribution model to estimate the probability of observing fewer than 3 harmful or inappropriate posts.
State the name and parameters of this distribution as part of your answer.
Question 3 (a)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
Use a probability distribution model to estimate the probability of observing fewer than 3 harmful or inappropriate posts.
State the name and parameters of this distribution as part of your answer.
Question 3 (a)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
Use a probability distribution model to estimate the probability of observing fewer than 3 harmful or inappropriate posts.
State the name and parameters of this distribution as part of your answer.
Question 3
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
Use a probability distribution model to estimate the probability of observing fewer than 3 harmful or inappropriate posts.
State the name and parameters of this distribution as part of your answer.
Question 3
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
Use a probability distribution model to estimate the probability of observing fewer than 3 harmful or inappropriate posts.
State the name and parameters of this distribution as part of your answer.
Question 3
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
Use a probability distribution model to estimate the probability of observing fewer than 3 harmful or inappropriate posts.
State the name and parameters of this distribution as part of your answer.
Question 3
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
Use a probability distribution model to estimate the probability of observing fewer than 3 harmful or inappropriate posts.
State the name and parameters of this distribution as part of your answer.
Graphics Calculator solutions are accepted too, and there may be a slight variation with rounding, which is accepted.
Question 3 (b)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
(b) To apply the distribution used in part (a) to model the number of harmful or inappropriate posts, an assumption of independence was made.
Describe this assumption in context, and whether it is valid to make this assumption for this situation.
Question 3 (b)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
(b) To apply the distribution used in part (a) to model the number of harmful or inappropriate posts, an assumption of independence was made.
Describe this assumption in context, and whether it is valid to make this assumption for this situation.
Question 3 (b)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
(b) To apply the distribution used in part (a) to model the number of harmful or inappropriate posts, an assumption of independence was made.
Describe this assumption in context, and whether it is valid to make this assumption for this situation.
Question 3 (b)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
(b) To apply the distribution used in part (a) to model the number of harmful or inappropriate posts, an assumption of independence was made.
Describe this assumption in context, and whether it is valid to make this assumption for this situation.
Independence assumption: the identification of inappropriate or harmful content in one post does not affect the probability of inappropriate or harmful content being identified in another post.
This assumption is unlikely to be valid because all 20 posts have been created by the same user and are likely to use similar language or grammar – if the model detects inappropriate content in one post it may be more likely to detect inappropriate content in another.
Question 3 (b)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
(b) To apply the distribution used in part (a) to model the number of harmful or inappropriate posts, an assumption of independence was made.
Describe this assumption in context, and whether it is valid to make this assumption for this situation.
“The automated system is used to screen 20 posts created by one user for harmful or inappropriate content”
Independence assumption: the identification of inappropriate or harmful content in one post does not affect the probability of inappropriate or harmful content being identified in another post.
This assumption is unlikely to be valid because all 20 posts have been created by the same user and are likely to use similar language or grammar – if the model detects inappropriate content in one post it may be more likely to detect inappropriate content in another.
Question 3 (b)
A social media platform checks user-generated content using an automated system to identify potentially harmful or inappropriate posts. A population of posts where 1 in 10 posts contain harmful or inappropriate content is screened.
(b) To apply the distribution used in part (a) to model the number of harmful or inappropriate posts, an assumption of independence was made.
Describe this assumption in context, and whether it is valid to make this assumption for this situation.
“The automated system is used to screen 20 posts created by one user for harmful or inappropriate content”
Independence assumption: the identification of inappropriate or harmful content in one post does not affect the probability of inappropriate or harmful content being identified in another post.
This assumption is unlikely to be valid because all 20 posts have been created by the same user and are likely to use similar language or grammar – if the model detects inappropriate content in one post it may be more likely to detect inappropriate content in another.
Question 3 (c) i
The system reports false positives, meaning that a proportion of harmless content is mistakenly identified as inappropriate.
How many false positives, on average, are reported by the system for each batch of 100 posts?
Question 3 (c) i
The system reports false positives, meaning that a proportion of harmless content is mistakenly identified as inappropriate.
How many false positives, on average, are reported by the system for each batch of 100 posts?
Question 3 (c) i
The system reports false positives, meaning that a proportion of harmless content is mistakenly identified as inappropriate.
How many false positives, on average, are reported by the system for each batch of 100 posts?
Question 3 (c) i
The system reports false positives, meaning that a proportion of harmless content is mistakenly identified as inappropriate.
How many false positives, on average, are reported by the system for each batch of 100 posts?
Question 3 (c) i
The system reports false positives, meaning that a proportion of harmless content is mistakenly identified as inappropriate.
How many false positives, on average, are reported by the system for each batch of 100 posts?
Question 3 (c) ii
The system reports false positives, meaning that a proportion of harmless content is mistakenly identified as inappropriate.
Question 3 (c) ii
The system reports false positives, meaning that a proportion of harmless content is mistakenly identified as inappropriate.
Question 3 (c) ii
The system reports false positives, meaning that a proportion of harmless content is mistakenly identified as inappropriate.
Question 3 (c) ii
The system reports false positives, meaning that a proportion of harmless content is mistakenly identified as inappropriate.
The Poisson model assumes that false positives are typically independent events whether one post is reported as a false positive in a batch does not affect another post being reported as being a false positive in another batch. The automated system being used has no memory of previous reports so its reporting of one false positive will be independent of the next report.
The Poisson model assumes that false positives in a batch would be expected to occur randomly and unpredictably. We assume the automated system selects posts for checking at random and assume that false positives are reported randomly within those selected.
The Poisson model assumes that the rate is proportional to the interval. It is assumed that the rate of reporting false positives in a batch of posts is 2.1 false positives per batch of 100 posts which is scalable to give a rate in a batch of 10, 50 100, 200, 500, 1000 posts and so on because of the automated nature of the system.
The Poisson model assumes that events cannot occur simultaneously. In this context, we are assuming the system is automated and processes one item at a time very quickly. Therefore, two false positives cannot be identified at exactly the same moment.
The Poisson model also assumes that the rate of events occurring remains constant over the given time or space interval. Since the automated system follows a fixed set of rules to identify harmful posts, we must assume that the rate at which it detects false positives within a batch must remain constant.
Question 3 (c) ii
The system reports false positives, meaning that a proportion of harmless content is mistakenly identified as inappropriate.
The Poisson model assumes that false positives are typically independent events whether one post is reported as a false positive in a batch does not affect another post being reported as being a false positive in another batch. The automated system being used has no memory of previous reports so its reporting of one false positive will be independent of the next report.
The Poisson model assumes that false positives in a batch would be expected to occur randomly and unpredictably. We assume the automated system selects posts for checking at random and assume that false positives are reported randomly within those selected.
The Poisson model assumes that the rate is proportional to the interval. It is assumed that the rate of reporting false positives in a batch of posts is 2.1 false positives per batch of 100 posts which is scalable to give a rate in a batch of 10, 50 100, 200, 500, 1000 posts and so on because of the automated nature of the system.
The Poisson model assumes that events cannot occur simultaneously. In this context, we are assuming the system is automated and processes one item at a time very quickly. Therefore, two false positives cannot be identified at exactly the same moment.
The Poisson model also assumes that the rate of events occurring remains constant over the given time or space interval. Since the automated system follows a fixed set of rules to identify harmful posts, we must assume that the rate at which it detects false positives within a batch must remain constant.
Question 3 (c) ii
The system reports false positives, meaning that a proportion of harmless content is mistakenly identified as inappropriate.
The Poisson model assumes that false positives are typically independent events whether one post is reported as a false positive in a batch does not affect another post being reported as being a false positive in another batch. The automated system being used has no memory of previous reports so its reporting of one false positive will be independent of the next report.
The Poisson model assumes that false positives in a batch would be expected to occur randomly and unpredictably. We assume the automated system selects posts for checking at random and assume that false positives are reported randomly within those selected.
The Poisson model assumes that the rate is proportional to the interval. It is assumed that the rate of reporting false positives in a batch of posts is 2.1 false positives per batch of 100 posts which is scalable to give a rate in a batch of 10, 50 100, 200, 500, 1000 posts and so on because of the automated nature of the system.
The Poisson model assumes that events cannot occur simultaneously. In this context, we are assuming the system is automated and processes one item at a time very quickly. Therefore, two false positives cannot be identified at exactly the same moment.
The Poisson model also assumes that the rate of events occurring remains constant over the given time or space interval. Since the automated system follows a fixed set of rules to identify harmful posts, we must assume that the rate at which it detects false positives within a batch must remain constant.
Question 3 (c) ii
The system reports false positives, meaning that a proportion of harmless content is mistakenly identified as inappropriate.
The Poisson model assumes that false positives are typically independent events whether one post is reported as a false positive in a batch does not affect another post being reported as being a false positive in another batch. The automated system being used has no memory of previous reports so its reporting of one false positive will be independent of the next report.
The Poisson model assumes that false positives in a batch would be expected to occur randomly and unpredictably. We assume the automated system selects posts for checking at random and assume that false positives are reported randomly within those selected.
The Poisson model assumes that the rate is proportional to the interval. It is assumed that the rate of reporting false positives in a batch of posts is 2.1 false positives per batch of 100 posts which is scalable to give a rate in a batch of 10, 50 100, 200, 500, 1000 posts and so on because of the automated nature of the system.
The Poisson model assumes that events cannot occur simultaneously. In this context, we are assuming the system is automated and processes one item at a time very quickly. Therefore, two false positives cannot be identified at exactly the same moment.
The Poisson model also assumes that the rate of events occurring remains constant over the given time or space interval. Since the automated system follows a fixed set of rules to identify harmful posts, we must assume that the rate at which it detects false positives within a batch must remain constant.
Question 3 (c) ii
The system reports false positives, meaning that a proportion of harmless content is mistakenly identified as inappropriate.
The Poisson model assumes that false positives are typically independent events whether one post is reported as a false positive in a batch does not affect another post being reported as being a false positive in another batch. The automated system being used has no memory of previous reports so its reporting of one false positive will be independent of the next report.
The Poisson model assumes that false positives in a batch would be expected to occur randomly and unpredictably. We assume the automated system selects posts for checking at random and assume that false positives are reported randomly within those selected.
The Poisson model assumes that the rate is proportional to the interval. It is assumed that the rate of reporting false positives in a batch of posts is 2.1 false positives per batch of 100 posts which is scalable to give a rate in a batch of 10, 50 100, 200, 500, 1000 posts and so on because of the automated nature of the system.
The Poisson model assumes that events cannot occur simultaneously. In this context, we are assuming the system is automated and processes one item at a time very quickly. Therefore, two false positives cannot be identified at exactly the same moment.
The Poisson model also assumes that the rate of events occurring remains constant over the given time or space interval. Since the automated system follows a fixed set of rules to identify harmful posts, we must assume that the rate at which it detects false positives within a batch must remain constant.
Question 3 (c) ii
The system reports false positives, meaning that a proportion of harmless content is mistakenly identified as inappropriate.
The Poisson model assumes that false positives are typically independent events whether one post is reported as a false positive in a batch does not affect another post being reported as being a false positive in another batch. The automated system being used has no memory of previous reports so its reporting of one false positive will be independent of the next report.
The Poisson model assumes that false positives in a batch would be expected to occur randomly and unpredictably. We assume the automated system selects posts for checking at random and assume that false positives are reported randomly within those selected.
The Poisson model assumes that the rate is proportional to the interval. It is assumed that the rate of reporting false positives in a batch of posts is 2.1 false positives per batch of 100 posts which is scalable to give a rate in a batch of 10, 50 100, 200, 500, 1000 posts and so on because of the automated nature of the system.
The Poisson model assumes that events cannot occur simultaneously. In this context, we are assuming the system is automated and processes one item at a time very quickly. Therefore, two false positives cannot be identified at exactly the same moment.
The Poisson model also assumes that the rate of events occurring remains constant over the given time or space interval. Since the automated system follows a fixed set of rules to identify harmful posts, we must assume that the rate at which it detects false positives within a batch must remain constant.
Two correct reasons justified in context.
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| | | | | | |
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| | | | | | |
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| | 97% = 0.97 | ||||
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
Any number to the power of zero is 1
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
The average number of false positives per 100 posts is approx. 3.5.
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
The average number of false positives per 100 posts is approx. 3.5.
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
The average number of false positives per 100 posts is approx. 3.5.
Question 3 (d)
A competing social media screening system states that at least one false positive is found in 97% of their batches of 100 posts.
Calculate the false positive rate for this screening system, and use this calculation to comment on the accuracy of the competing system compared to the original system from part (c).
| 0 | 1 | 2 | 3 | 4 | … |
| 0.03 | 97% = 0.97 | ||||
The average number of false positives per 100 posts is approx. 3.5.
With the original system, the false positive rate is 2.1 false positives per 100 posts.
The competing system appears to be less accurate less reliable as it has a higher false positive rate at 3.5 false positives per 100 posts i.e. it is identifying a post as having harmful content when it doesn’t have.