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Probability
A quantitative measure of the likelihood that a random phenomenon or chance behavior will occur.
Empirical Probability
Probability derived from observed data, calculated as the number of times an event occurs divided by the total number of trials.
Sample Space (S)
The collection of all possible outcomes of a probability experiment.
Disjoint Events
Events that cannot occur simultaneously.
Certain Event
An event that is certain to occur, with a probability of 1.
Impossible Event
An event that cannot occur, with a probability of 0.
Law of Large Numbers
As the number of repetitions of a probability experiment increases, the observed frequencies of outcomes converge to the theoretical probabilities.
Subjective Probabilities
Probabilities derived from personal judgment or belief rather than empirical data.
Addition Rule
In the context of disjoint events, the probability of either event E or F occurring is the sum of their individual probabilities.
Complement Rule
The probability of the complement of an event E is equal to 1 minus the probability of E.
Conditional Probability
The probability of an event F occurring given that event E has occurred.
Permutations
Ordered arrangements of objects where the sequence matters.
Combinations
Selections of objects where the order does not matter.
General Addition Rule
For any two events E and F, the probability of either E or F occurring is given by P(E) + P(F) - P(E and F).
Independence
Two events are independent if the occurrence of one does not affect the probability of the other occurring.
Multiplication Rule for Independent Events
The probability of both events E and F occurring is the product of their individual probabilities.
Empirical Method
A method of calculating probability based on frequency data from experiments.
Classical Method
A method of calculating probability based on reasoning or intuition regarding equally likely outcomes.
Bayes's Rule
A theorem that describes how to update probabilities based on new evidence.
Note 
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