CBSE Class 9 Artificial Intelligence (402) Unit 3 – Math for AI (Statistics & Probability) Important Subjective Questions with Answers
Class 9 · Artificial Intelligence
CBSE Class 9 Artificial Intelligence (402)
Unit 3 – Math for AI (Statistics & Probability)
These important subjective questions are prepared according to the latest CBSE competency-based examination pattern and are completely based on the Class 9 Artificial Intelligence Facilitator Handbook. The questions include competency-based, case-study, application-based and Higher Order Thinking Skills (HOTS).
Instructions
- Total Questions : 25
- This section contains 10 Questions of 2 Marks each.
- Read every question carefully.
- Support your answers with suitable examples wherever possible.
Section A – 2 Mark Questions
Q1. Define the role of Mathematics in Artificial Intelligence. Mention any two reasons why Mathematics is important for AI.
Answer:
Mathematics is the foundation of Artificial Intelligence because it helps machines recognize patterns, analyse data and make intelligent decisions.
Importance of Mathematics in AI:
- Helps AI identify patterns in data.
- Enables AI models to make predictions and decisions accurately.
Example: Google Maps predicts the fastest route by analysing mathematical patterns in traffic data.
Q2. Explain the relationship between Mathematics and Artificial Intelligence with one suitable example.
Answer:
Mathematics studies patterns, while Artificial Intelligence uses these mathematical patterns to learn from data and solve problems.
Example:
In the number series 2, 4, 6, 8, 10, AI recognizes the pattern of adding 2 and predicts that the next number will be 12.
Q3. Name any four mathematical concepts used in Artificial Intelligence.
Answer:
- Statistics
- Probability
- Calculus
- Linear Algebra
Each mathematical concept helps AI solve different types of real-world problems.
Q4. Differentiate between Statistics and Probability.
Answer:
| Statistics | Probability |
|---|---|
| Analyses existing data. | Predicts future events. |
| Helps in decision making. | Measures the likelihood of an event. |
| Example: Average Marks. | Example: Chance of Rain. |
Q5. Mention any two real-life applications of Statistics in Artificial Intelligence.
Answer:
- Weather Forecasting.
- Disease Prediction.
- Sports Performance Analysis.
- Disaster Management.
(Any two)
Q6. What is Probability? State the probability of an impossible event and a certain event.
Answer:
Probability is the mathematical measure of how likely an event is to occur.
- Probability of an Impossible Event = 0
- Probability of a Certain Event = 1
Q7. Explain Continuous Pattern Recognition with the help of one practical example.
Answer:
Pattern recognition means identifying relationships or regular changes in data.
Example:
If a company's profit increases from ₹1000 to ₹1500 and then ₹2000, AI identifies the increasing pattern and predicts future profits.
Q8. Mention any two AI applications where Probability is widely used.
Answer:
- Weather Forecasting.
- Traffic Prediction.
- Sports Performance Prediction.
- Risk Analysis.
(Any two)
Q9. Write the probability formula and explain its terms.
Answer:
Formula:
P(A) = Number of Favourable Outcomes / Total Number of Possible Outcomes
Where:
- P(A) = Probability of Event A
- Favourable Outcomes = Desired outcomes
- Total Possible Outcomes = Total number of outcomes
Q10. Why do AI systems require Mathematics instead of only programming?
Answer:
Programming provides instructions to computers, whereas Mathematics enables AI to analyse data, identify patterns, make predictions and improve decision-making.
Without Mathematics, AI models cannot learn from data effectively.
Section B – 3 Mark Questions
Q11. (Competency Based)
A supermarket records the daily number of customers visiting the store for one month. The management wants to predict the expected number of customers for the coming weekend.
Answer the following:
- Which mathematical concept of AI will be mainly used?
- Why is this concept useful?
- Mention one benefit of using AI in this situation.
Answer:
(i) Statistics.
(ii)
Statistics analyses past customer data to identify trends and patterns that help AI make predictions.
(iii)
The supermarket can prepare enough stock and staff in advance, reducing shortages and improving customer service.
Q12. (Case Study)
A weather department collects temperature, humidity, rainfall and wind speed data every day. AI analyses this information to predict whether it will rain tomorrow.
Answer the following:
- Name the mathematical concepts used in this project.
- Why is Statistics required?
- Why is Probability required?
Answer:
(i)
- Statistics
- Probability
(ii)
Statistics helps analyse historical weather records and identify weather patterns.
(iii)
Probability estimates the likelihood of rainfall based on analysed weather conditions.
Q13. Explain the statistical process with the help of suitable examples.
Answer:
| Stage | Description | Example |
|---|---|---|
| Collection | Gathering raw data. | Collecting examination marks. |
| Cleaning & Exploring | Removing errors and arranging data. | Removing duplicate student records. |
| Analysis | Studying data to identify patterns. | Calculating average marks. |
| Decision Making | Taking decisions based on analysed data. | Planning extra classes for weak students. |
Q14. (Application Based)
A cricket team wants to improve its performance by analysing players' previous match statistics.
Explain how Statistics helps the team management make better decisions.
Answer:
- Identifies the strengths and weaknesses of players.
- Calculates batting and bowling averages.
- Predicts future performance based on previous records.
- Helps select the best playing eleven.
Q15. (Competency Based)
A city administration wants to estimate traffic congestion during office hours using AI.
Answer the following:
- Which mathematical concept is mainly used?
- Which type of historical data will be collected?
- How will AI help citizens?
Answer:
(i) Probability.
(ii)
- Previous traffic records
- Vehicle count
- Peak hour timings
- Road conditions
(iii)
AI predicts traffic congestion and recommends the fastest routes, saving time and fuel.
Q16. (HOTS)
Explain why Pattern Recognition is considered the foundation of Artificial Intelligence. Support your answer with any three suitable examples.
Answer:
Pattern Recognition enables AI systems to identify relationships hidden within data.
Examples:
- Recognising faces in smartphone Face Unlock.
- Predicting future profits from previous sales records.
- Identifying weather trends for rainfall prediction.
Without pattern recognition, AI cannot learn from data or make intelligent predictions.
Q17. (Case Study)
A disaster management department collects rainfall data, river water levels and satellite images before issuing flood warnings.
Answer the following:
- Which mathematical concept helps analyse historical data?
- Which mathematical concept predicts future floods?
- State one benefit of using AI in disaster management.
Answer:
(i) Statistics.
(ii) Probability.
(iii)
AI provides early warnings, helping authorities protect lives and reduce property damage.
Q18. (Competency Based)
A school analyses students' reading habits using AI. The system collects the number of books issued, reading time and examination marks to identify students who need additional academic support.
Answer the following:
- Which mathematical concept is mainly used?
- Why is Mathematics necessary for this AI system?
- How can the school benefit from this analysis?
Answer:
(i) Statistics.
(ii)
Mathematics helps AI analyse patterns and relationships among students' reading habits and academic performance.
(iii)
Teachers can identify students requiring additional support and provide personalised learning plans to improve academic performance.
Section C – 4 Mark Questions
Q19. (Case Study Based)
A weather forecasting department collects temperature, humidity, air pressure, wind speed and rainfall data from different cities every day. The data is analysed using Artificial Intelligence to predict weather conditions and issue alerts to citizens.
Answer the following:
- Which mathematical concepts are mainly used in this project?
- Explain how Statistics helps in this AI application.
- Explain how Probability helps in weather prediction.
- State one benefit of using AI in weather forecasting.
Answer:
(i) Mathematical Concepts
- Statistics
- Probability
(ii) Role of Statistics
Statistics helps analyse historical weather records, identify seasonal trends and compare current weather conditions with previous years.
(iii) Role of Probability
Probability estimates the likelihood of future weather events such as rainfall, storms or snowfall.
(iv) Benefit
Early weather predictions help people prepare for natural disasters, protect crops and reduce loss of life and property.
Q20. Explain how Mathematics supports Artificial Intelligence. Describe the role of Statistics, Probability, Calculus and Linear Algebra with suitable examples.
Answer:
| Mathematical Concept | Role in AI | Example |
|---|---|---|
| Statistics | Explores and analyses data. | Finding average marks of students. |
| Probability | Predicts future events. | Weather forecasting. |
| Calculus | Improves AI models during training. | Finding the slope of a graph. |
| Linear Algebra | Represents and processes data mathematically. | Finding unknown values in datasets. |
These mathematical concepts enable AI systems to analyse patterns, learn from data and make accurate predictions.
Q21. (Competency Based)
A cricket board wants to develop an AI system that predicts the performance of players in upcoming matches. The AI system analyses previous scores, batting averages, strike rates and recent match performance.
Answer the following:
- Which mathematical concept is mainly used for analysing player performance?
- Which mathematical concept helps predict future scores?
- How does AI help selectors?
- State one limitation of relying completely on AI predictions.
Answer:
(i) Statistics.
(ii) Probability.
(iii)
AI analyses historical performance and recommends the best players for selection based on data-driven insights.
(iv)
Unexpected situations such as injuries, weather conditions or player fitness cannot always be predicted accurately by AI.
Q22. (HOTS)
Artificial Intelligence can recognise patterns much faster than humans.
Explain the importance of Pattern Recognition in AI by discussing any four practical applications.
Answer:
Applications of Pattern Recognition
- Face Recognition for smartphone security.
- Fraud Detection in banking transactions.
- Weather Forecasting using climate patterns.
- Medical Diagnosis through X-ray and MRI image analysis.
Pattern Recognition enables AI systems to learn from previous data and make intelligent predictions automatically.
Q23. (Application Based)
A school wants to analyse students' examination performance using AI. Teachers collect marks obtained in Unit Tests, Half-Yearly Examination and Annual Examination over three years.
Answer the following:
- Describe the statistical process that should be followed.
- How will AI help teachers identify weak students?
- State one benefit of using AI instead of manual calculations.
- Suggest one graphical method for presenting the results.
Answer:
(i) Statistical Process
- Collect examination data.
- Clean and organise the data.
- Analyse trends and averages.
- Make academic decisions based on the results.
(ii)
AI compares students' performance over multiple examinations and identifies those who consistently perform below the expected level.
(iii)
AI analyses thousands of records quickly and accurately, reducing manual effort and human errors.
(iv)
Bar Graph or Line Graph.
Q24. (Case Study Based)
A navigation application analyses millions of GPS records every day to estimate traffic conditions on different roads. Based on previous traffic patterns and current vehicle movement, the application suggests the fastest route to users.
Answer the following:
- Which mathematical concept analyses historical traffic data?
- Which mathematical concept predicts future traffic conditions?
- Why is pattern recognition important in this application?
- State one advantage of using AI in navigation systems.
Answer:
(i) Statistics.
(ii) Probability.
(iii)
Pattern recognition enables AI to identify regular traffic behaviour during different times of the day and predict congestion levels.
(iv)
AI helps users save time, reduce fuel consumption and select the best available route.
Q25. (Integrated Competency Question)
A smart city project uses AI to improve public services. The AI system predicts rainfall, monitors traffic congestion, analyses disease outbreaks and studies electricity consumption patterns.
Answer the following:
- Identify any four applications of Mathematics used in this project.
- Explain how Statistics contributes to decision making.
- Explain the role of Probability in prediction.
- Why is Mathematics considered the foundation of Artificial Intelligence?
Answer:
(i) Applications
- Weather Forecasting
- Traffic Prediction
- Disease Prediction
- Electricity Consumption Analysis
(ii) Statistics
Statistics analyses historical data, identifies trends and provides useful information for planning and decision making.
(iii) Probability
Probability estimates the chances of future events such as rainfall, traffic congestion or disease outbreaks.
(iv) Importance of Mathematics in AI
- Helps AI identify patterns.
- Supports data analysis.
- Enables prediction and intelligent decision making.
- Forms the mathematical foundation for AI algorithms.
Revision Tips
- Understand why Mathematics is called the foundation of AI.
- Revise the four mathematical concepts: Statistics, Probability, Calculus and Linear Algebra.
- Learn the complete statistical process: Collection, Cleaning, Analysis and Decision Making.
- Remember the applications of Statistics in sports, weather forecasting, disaster management and disease prediction.
- Revise the probability formula and the probability scale.
- Remember that an impossible event has probability 0 and a certain event has probability 1.
- Practice identifying AI applications that use Statistics and Probability.
- Focus on competency-based and case-study questions related to real-life AI applications.
★★★★★ End of Class 9 AI Unit 3 Subjective Question Bank with Answers ★★★★★