What is Probability?

7.1 WHAT IS PROBABILITY?

Probability is a mathematical measure used to express the likelihood or chance that a particular event will occur. Unlike physical measurements such as length, area, or volume, probability quantifies uncertainty and randomness in events. Everyday questions such as "Is it going to rain today?", "Will our school win the hockey match tomorrow?", or "Will I be chosen in the lucky draw?" are examples of events involving chance. These are called random events because although we know the possible outcomes, we cannot predict with certainty which outcome will happen. For example, it may rain or not rain today; the school hockey team may win, lose, or draw; and any student’s name may be drawn in the lucky draw. The uncertainty arises because of the element of chance or randomness involved. People often express their belief about the likelihood of an event using terms like impossible, certain, less likely, more likely, or equally likely. These expressions are subjective and based on personal interpretation of evidence, such as weather conditions or past experiences. For instance, one friend may say it is unlikely to rain because the sun is shining, while another may think rain is possible because it is hot and humid. This is called subjective probability, reflecting personal judgment rather than objective measurement. Probability deals with uncertainty and chance, which are common in real life. As society becomes more complex, many questions have multiple possible answers rather than fixed ones. Therefore, learning how to estimate probability objectively, based on evidence rather than opinion, is important. This chapter introduces the concept of randomness, the probability scale, and methods to measure probability objectively.

• Probability measures the likelihood of an event occurring.
• Random events have known possible outcomes but unpredictable results.
• Subjective probability is based on personal judgment and evidence interpretation.
• Probability helps quantify uncertainty and chance in real-life situations.
• Understanding probability is important for decision-making in uncertain conditions.
• 📌 Probability: A measure of how likely an event is to occur.
• 📌 Random event: An event with uncertain outcome but known possible results.
• 📌 Subjective probability: Probability based on personal judgment or evidence.

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.

• Randomness means outcomes cannot be predicted exactly despite knowing all possibilities.
• Random experiments can be repeated with unpredictable results each time.
• Examples: tossing a coin, rolling a die, lucky draw.
• Randomness ensures fairness in decisions like coin toss in cricket.
• Natural phenomena like rain are random due to complex influencing factors.
• 📌 Random experiment: An action or process with unpredictable outcomes that can be repeated.
• 📌 Randomness: The property of unpredictability in outcomes.