Probability | Class 12 Mathematics Notes

Random Experiment, Sample Space and Events

A random experiment is a process or action that leads to one of several possible outcomes, where the exact outcome cannot be predicted with certainty in advance. For example, tossing a coin, rolling a die, or drawing a card from a well-shuffled deck are random experiments. The set of all possible outcomes of a random experiment is called the sample space, denoted by S. Each outcome in the sample space is called a sample point. For instance, when tossing a coin, the sample space is S = {Head, Tail}. When rolling a die, the sample space is S = {1, 2, 3, 4, 5, 6}. An event is any subset of the sample space. It can be a single outcome (simple event) or a collection of outcomes (compound event). For example, in rolling a die, the event 'getting an even number' is E = {2, 4, 6}. Events can be classified as certain (the whole sample space), impossible (empty set), simple, or compound. Events can also be mutually exclusive if they cannot occur simultaneously. Understanding these concepts is essential for defining and calculating probabilities. The section also introduces set operations such as union, intersection, and complement of events, which are used to describe combined events and their probabilities.

📊 Diagram: Venn diagrams illustrating sample space and events: circles representing events inside a rectangle representing the sample space, showing union, intersection, and complement.

🧪 Activity: Activity: Listing sample spaces for different random experiments such as tossing two coins, rolling two dice, and drawing cards.

🔗 Connection: Prepares for the Classical Definition of Probability by establishing the fundamental concepts of sample space and events.