CBSE Class 9 Math for AI (Statistics & Probability) Important Subjective Questions & Answers (2026–27) | Unit 3 Artificial Intelligence

Answer:

Mathematics is the foundation of Artificial Intelligence because it helps AI systems identify patterns, analyze data, make predictions, and solve problems.

AI models use mathematical concepts to describe relationships between different data values, enabling machines to learn from data and make intelligent decisions.

Answer:

The four core branches of Mathematics used in AI are:

• Statistics
• Linear Algebra
• Probability
• Calculus

Role of Statistics: Helps collect, organize, analyze, and interpret data.

Role of Probability: Helps AI estimate the likelihood of future events and make predictions.

Answer:

Pattern Recognition enables AI systems to identify similarities, trends, and relationships in data.

For example, an AI system can distinguish between images of a dog and a cat by recognizing patterns in their shapes, ears, eyes, and body features. Similarly, AI can recognize handwritten digits or detect diseases from medical images.

Answer:

Linear Algebra helps AI work with large datasets by representing information as vectors and matrices.

It is used to find missing values, perform calculations on data, process images, and support machine learning algorithms efficiently.

Answer:

Machines cannot understand information like humans. They process data in the form of numbers and binary values (0s and 1s).

Therefore, images, text, speech, and videos must be converted into mathematical representations so that AI models can recognize patterns and make accurate decisions.

Answer:

Statistics is the science of collecting, organizing, analyzing, interpreting, and presenting data to make meaningful decisions.

The four steps of the statistical process are:

1. Data Collection
2. Data Cleaning and Exploration
3. Data Analysis
4. Decision Making

Answer:

Statistics helps disaster management teams analyze population, weather conditions, infrastructure, and available resources.

Based on statistical analysis, authorities can prepare evacuation plans, allocate relief materials, predict disaster impact, and improve recovery efforts.

Answer:

Governments analyze health records, disease reports, vaccination data, and population statistics to identify disease trends.

This helps them predict disease outbreaks, plan vaccination campaigns, improve healthcare facilities, and provide timely medical assistance.

Answer:

Data Cleaning removes duplicate records, missing values, incorrect entries, and unnecessary information from a dataset.

Clean data improves the accuracy of statistical analysis and helps AI models make reliable predictions.

Answer:

Mean is the average value of a dataset. It is calculated by adding all the observations and dividing the total by the number of observations.

Formula:

Mean = Sum of all observations ÷ Number of observations

The mean helps identify the typical value of a dataset and is widely used to compare data and make informed decisions.

Answer:

Weather forecasting systems analyze historical weather records along with current temperature, humidity, wind speed, and atmospheric pressure.

By comparing present conditions with past statistical patterns, computers can predict future weather conditions with greater accuracy.

Answer:

Probability is the measure of the chance that an event will occur.

Formula:

Probability (P) = Number of Favourable Outcomes ÷ Total Number of Possible Outcomes

The value of probability always lies between 0 and 1.

Answer:

An Equal Probability Event is an event where all possible outcomes have the same chance of occurring.

Example: Tossing a fair coin. The probability of getting Heads and Tails is equal, that is, 1/2 each.

Answer:

Probability helps estimate the likelihood of traffic congestion by analyzing historical traffic data, road conditions, weather, and travel patterns.

Navigation applications use these predictions to suggest the fastest routes and estimate travel time.

Answer:

Sports analysts use probability by studying previous match results, player performance, weather conditions, team rankings, and other statistics.

AI combines these factors to estimate the probability of each team winning, losing, or drawing a match.

Answer:

The prediction is based on Probability.

Meteorologists compare current weather conditions with similar situations from past records. If it rained in about 70 out of 100 similar cases, the probability of rainfall is estimated as 70%.

Answer:

Artificial Intelligence understands data only in numerical form. Mathematics provides the tools required to represent data, identify patterns, calculate relationships, measure uncertainty, and improve AI models.

Without mathematical concepts such as Statistics, Probability, Linear Algebra, and Calculus, AI systems cannot learn from data or make intelligent predictions.

Answer:

The Mode is the value that appears most frequently in a dataset.

Here, the observations are:

• Red = 3
• Black = 4
• White = 7

Since White has the highest frequency (7), the Mode is White.

This means that white is the most commonly observed car colour during the survey.

Answer:

AI models learn mathematical relationships from the data provided during training. If the training data is inaccurate, incomplete, or biased, the model learns incorrect patterns.

As a result, the AI system produces unfair or inaccurate predictions, which may lead to discrimination or wrong decisions. Therefore, AI models should always be trained using clean, balanced, and unbiased datasets.

Answer:

The possible outcomes when rolling a die are:

{1, 2, 3, 4, 5, 6}

The prime numbers are:

{2, 3, 5}

Total Outcomes = 6

Favourable Outcomes = 3

Probability = Favourable Outcomes ÷ Total Outcomes

P = 3/6 = 1/2 = 0.5

Therefore, the probability of getting a prime number is 1/2.

Answer:

Simple arithmetic performs basic calculations, whereas Calculus helps measure the rate of change in mathematical functions.

AI algorithms use Calculus to calculate gradients, reduce errors, and continuously improve model accuracy during training. This process helps the AI model learn efficiently and achieve better performance.

Answer:

Step 1: Calculate the total number of cases.

5 + 7 + 9 + 22 + 11 = 54

Step 2: Calculate the sum of (Age × Number of Cases).

(10 × 5) + (12 × 7) + (14 × 9) + (15 × 22) + (16 × 11)

= 50 + 84 + 126 + 330 + 176

= 766

Step 3: Apply the Mean Formula.

Mean = Total of (Age × Cases) ÷ Total Cases

Mean = 766 ÷ 54 ≈ 14.19 years

Therefore, the average (Mean) age is approximately 14.19 years.