Mathematics
Introduction to Probability
प्रायिकता का परिचय
This Class 9 Mathematics chapter introduces probability as a way to measure how likely an uncertain event is to occur. Students explore random experiments, outcomes, sample spaces, and events through familiar examples such as tossing coins, rolling dice, and selecting objects. They learn to identify favourable outcomes and calculate the probability of an event when outcomes are equally likely, using the ratio of favourable outcomes to total outcomes. The chapter also develops an understanding that probability lies between 0 and 1, helping students interpret impossible, possible, and certain events.
1Randomness
यादृच्छिकता
In Class 9 Mathematics, this topic introduces randomness as the uncertainty involved in the results of an experiment. Students learn to distinguish random experiments from predictable situations, identify possible outcomes, and describe events using simple examples such as coins, dice, or everyday observations. The topic builds the foundation for understanding probability by connecting observed outcomes and patterns with the idea of chance, while encouraging clear reasoning about what can—and cannot—be predicted before an experiment is performed.
0 questionsProbability scale
प्रायिकता मापनी
In this Class 9 Mathematics topic from Introduction to Probability, students learn how the probability scale represents the likelihood of an event. They understand that probability ranges from 0 to 1, where 0 means an impossible event and 1 means a certain event. The topic also explains how values between 0 and 1 describe varying chances and how probability can be written as fractions, decimals, or percentages when analysing simple events.
0 questionsEmpirical probability
प्रायोगिक प्रायिकता
Empirical Probability introduces Class 9 students to estimating the chance of an event from actual observations or repeated trials. In the Mathematics chapter Introduction to Probability, students learn to record outcomes, count how often a favourable event occurs, and calculate experimental probability as favourable outcomes divided by total trials. The topic also shows why results may vary in different experiments and how larger numbers of trials can give a more reliable estimate of an event’s likelihood.
0 questionsTheoretical probability
सैद्धांतिक प्रायिकता
In this Class 9 Mathematics topic from Introduction to Probability, students learn how to predict the likelihood of events using a theoretical approach. They explore sample spaces, outcomes, events, and equally likely results, then apply the formula: probability = number of favourable outcomes ÷ total number of possible outcomes. Through simple examples involving coins, dice, cards, and everyday situations, students practise identifying outcomes, calculating probabilities, and expressing results as fractions, decimals, or percentages. The topic also builds a clear understanding of why probability lies between 0 and 1.
0 questionsSample space
नमूना समष्टि
In Class 9 Mathematics, the topic Sample Space introduces the complete set of all possible outcomes of a random experiment. Students learn to describe experiments such as tossing coins, rolling dice, or drawing objects, represent their outcomes systematically, and distinguish between an individual outcome and the full sample space. As part of Introduction to Probability, this concept helps students identify events and prepare for finding their probability by comparing favourable outcomes with the total number of equally likely outcomes.
0 questionsEvents
घटनाएँ
In Class 9 Mathematics, this topic introduces events as outcomes or collections of outcomes in a random experiment. Students learn to identify the sample space, describe simple events, and decide whether a given outcome belongs to an event. They connect favourable outcomes with the occurrence of an event and use this understanding to interpret basic probability situations, such as tossing coins, rolling dice, or selecting objects. The topic builds a clear foundation for calculating and explaining probability.
0 questionsTree diagrams
वृक्ष आरेख
Tree diagrams in Class 9 Mathematics provide a clear way to represent the possible outcomes of successive events in the chapter Introduction to Probability. Students learn to begin with an initial outcome, extend branches for each following possibility, and read the complete set of outcomes from the diagram. They also connect branches with sample spaces and use simple probability ideas to organise and analyse situations involving two or more stages.
0 questionsTables of outcomes
परिणामों की सारणियाँ
In this Class 9 Mathematics topic from Introduction to Probability, students learn how to list and organize all possible outcomes of simple experiments using tables. They explore examples such as coin tosses, dice rolls, and selecting objects, identify the sample space, and distinguish individual outcomes from events. The topic builds a clear foundation for counting outcomes and understanding how probability is represented in an organized, easy-to-read form.
0 questions