What is Probability? | Class 9 Mathematics Notes

7.1.1 What is Randomness?

Randomness refers to situations or actions where the exact outcome cannot be predicted in advance, even though all possible outcomes are known. Examples include tossing a coin or rolling a die. In these experiments, each trial can produce different results unpredictably. For instance, tossing a coin can result in heads or tails, but it is impossible to know which will occur on any single toss. Similarly, rolling a die can yield any number from 1 to 6, but the exact number on a particular roll is unknown beforehand.

Such unpredictable observations are called random experiments or trials. The lucky draw example, where a student is chosen randomly from a set of names, is also a random experiment because the outcome cannot be predicted and every student has an equal chance of selection. Random experiments can be repeated multiple times, and each trial is independent of the previous ones.

Randomness is important because it ensures fairness and unpredictability in many real-life scenarios. For example, in cricket, a coin toss is used to decide which team bats first because it is a fair and unbiased method, relying on randomness. Probability is the branch of mathematics that studies randomness and quantifies the likelihood of different outcomes in random experiments.

Random events like rain are considered random because they depend on complex and sensitive atmospheric factors such as temperature, humidity, wind, and pressure. These factors make it impossible to predict rain with absolute certainty, but probability allows us to estimate the likelihood based on patterns and data.

📊 Diagram: No specific diagram in this subsection, but earlier figures illustrate coin toss and die roll as examples of random experiments.

🧪 Activity: Think and Reflect: Ask a friend to predict the outcome of a ₹1 coin toss. Notice that the friend can guess heads or tails but cannot be certain, illustrating randomness.

🔗 Connection: This section sets the foundation for understanding the probability scale, which quantifies the likelihood of random events.