Learning Objectives
- Understand the concept of Sample Space and Events as the universal set for an experiment and define events as subsets of this space, including impossible, sure, simple, and compound events.
- Apply Algebra of Events using set operations like union, intersection, and complement, and comprehend mutually exclusive and exhaustive events.
- Grasp the Axiomatic Probability approach, defining probability as a function satisfying non-negativity, normalization, and additivity for mutually exclusive events.
- Calculate the Probability of Events using the axiomatic approach, including probabilities of 'A or B', 'not A', and equally likely outcomes.
- Analyze Mutually Exclusive and Exhaustive Events to understand events that cannot occur simultaneously and sets of events covering all possible outcomes.
- Utilize formulas for Probability of Union and Complement of Events, such as and , with Venn-diagram interpretation.
- Determine probabilities in Equally Likely Outcomes and Classical Probability scenarios using for dice, coins, cards, and other selections.
- Validate Assignment of Probabilities ensuring and total probability equals 1.
- Solve Combinatorics-Based Probability Problems using arrangements and combinations for scenarios like committees, lotteries, and card hands.
- Apply the formula for Probability of Three Events such as and related event-union problems.