Classical Probability Basics

Classical Probability

Definition

• Classical probability is a mathematical concept that measures the likelihood of an event occurring based on the number of favorable outcomes and total possible outcomes.
• It is also known as "a priori probability" or "Laplace's definition of probability".

Formula

• The probability of an event A is denoted as P(A) and is calculated as:

P(A) = Number of favorable outcomes / Total number of possible outcomes

Key Assumptions

• The outcomes are equally likely to occur.
• The outcomes are mutually exclusive (cannot occur simultaneously).
• The outcomes are exhaustive (cover all possible outcomes).

Example

• A fair six-sided die is rolled. What is the probability of rolling a 4?
  • Number of favorable outcomes: 1 (rolling a 4)
  • Total number of possible outcomes: 6 (1, 2, 3, 4, 5, 6)
  • P(rolling a 4) = 1/6

Properties

• The probability of an event A is a number between 0 and 1, inclusive.
• The probability of the sample space (total possible outcomes) is 1.
• The probability of the null event (impossible event) is 0.

Applications

• Classical probability is used in many areas, including:
  • Games of chance (e.g., lottery, casino games)
  • Insurance and actuarial science
  • Quality control and reliability engineering