Classical Probability and Probability Properties
This page delves deeper into probability theory, focusing on classical probability and the fundamental properties of probability functions.
Classical probability is introduced as a scenario where all outcomes of an experiment are equally likely. The formula P(A) = |A| / |Ω| is presented, where |A| represents the number of favorable outcomes and |Ω| is the total number of possible outcomes.
Example: In a fair coin toss, the probability of getting heads is 1/2, as there is one favorable outcome (heads) out of two possible outcomes (heads or tails).
The page then outlines the key properties of probability functions:
- Probability values are always between 0 and 1 inclusive.
- The probability of an impossible event is 0, while the probability of the entire sample space is 1.
- For mutually exclusive events, the probability of their union is the sum of their individual probabilities.
Vocabulary: Mutually exclusive events are events that cannot occur simultaneously.
Additional properties are presented, including the relationship between the probabilities of an event and its complement, and formulas for calculating probabilities of unions and set differences of events.
