Classical Probability

Classical Probability

Definition

• Classical probability is a measure of the likelihood of an event occurring, based on the number of favorable outcomes and the total number of possible outcomes.
• It is also known as "a priori probability" or "theoretical probability".

Formula

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

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

Key Concepts

• Sample Space: The set of all possible outcomes of an experiment.
• Event: A set of one or more outcomes of an experiment.
• Favorable Outcomes: The number of outcomes in the event set.
• Total Number of Possible Outcomes: The total number of outcomes in the sample space.

Properties

• Non-Negativity: 0 ≤ P(A) ≤ 1
• Normalization: P(S) = 1, where S is the sample space
• Additivity: P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where A and B are events

Examples

• Rolling a fair six-sided die:
  • Sample space: {1, 2, 3, 4, 5, 6}
  • Event: rolling an even number
  • Favorable outcomes: {2, 4, 6}
  • P(even) = 3/6 = 1/2
• Drawing a card from a standard deck of 52 cards:
  • Sample space: {52 possible cards}
  • Event: drawing a heart
  • Favorable outcomes: {13 hearts}
  • P(heart) = 13/52 = 1/4