Ch 14 approaches probability axiomatically (Kolmogorov's axioms) rather than just as a ratio. Students learn about sample spaces, events, types of events, the addition theorem, and complementary events.
A random experiment has unpredictable outcomes. The sample space S is the set of all possible outcomes. An event is a subset of S. Types: simple event (one outcome), compound event, mutually exclusive events (can't occur simultaneously), exhaustive events.
Axioms: P(S) = 1, 0 ≤ P(E) ≤ 1 for any event E, P(A∪B) = P(A) + P(B) for mutually exclusive A, B. If outcomes are equally likely, P(E) = n(E)/n(S).
For any events A, B: P(A∪B) = P(A) + P(B) − P(A∩B). If mutually exclusive: P(A∪B) = P(A) + P(B). Complement: P(A') = 1 − P(A).
Download: https://ncert.nic.in/textbook/pdf/kemh114.pdf | Complete book: https://ncert.nic.in/textbook/pdf/kemh1ps.zip
Two events are mutually exclusive if they cannot occur at the same time — their intersection is empty: P(A∩B) = 0. Example: getting "heads" and "tails" on a single coin toss. For mutually exclusive events: P(A∪B) = P(A) + P(B).
Book a Trial + Diagnostic session. Get a personalized Learning Path with clear milestones, tutor match, and a plan recommendation — all within 24 hours.
Book Trial + Diagnostic →