Chapter 14: Probability
Theoretical vs. Experimental Probability
This chapter introduces the concept of probability, focusing mainly on theoretical (classical) probability. Theoretical probability assumes equally likely outcomes and is defined as:
P(E)= Favourable outcomesTotal possible outcomes
Unlike experimental probability, which relies on repeating real-life trials (e.g., tossing a coin many times), theoretical probability uses logic and assumptions to calculate the chance of events. The chapter emphasizes that probabilities range between 0 (impossible event) and 1 (certain event), and that the sum of probabilities of all possible outcomes in an experiment is always 1.
Key Concepts and Examples
The chapter illustrates probability using relatable examples: tossing coins, throwing dice, drawing cards, and selecting marbles. It explains elementary events, complementary events, and uses scenarios like spinning a wheel or picking names to reinforce concepts. It also covers how to handle events with more than one favorable outcome, and how probabilities of multiple events relate (e.g., P(E) + P(not E) = 1). Examples include calculating the probability of getting a head or tail, drawing a red ball, or selecting a non-defective item.
Geometry-Based Probability and Real-Life Situations
Beyond discrete outcomes, the chapter briefly explores geometric probability where outcomes lie on a continuous scale, like a point falling randomly inside a region. It shows how probability can be calculated as the ratio of favorable area (or length) to total area. Practical examples such as games, missing helicopters, and shirts with defects connect theory to everyday applications. The chapter ends with a variety of exercises to test understanding across both basic and applied contexts.