Evaluate Probability

Evaluate Probability

Evaluating Probability

Definitions and Concepts

  • Probability is a mathematical measure quantifying the likelihood that a specific event will occur within a defined circumstance.
  • The probability of a single event is valued between 0 to 1 (inclusive), where 0 indicates that an event has no chance of occurrence and 1 means the event is certain to occur.
  • Events are deemed to be mutually exclusive if the occurrence of one event excludes the possibility of occurrence of the other. Mathematically, in a string of mutually exclusive events, the probability of two events happening simultaneously is zero.

Basic Evaluations

  • The probability of a certain event happening is always 1.
  • The probability of an impossible event is always 0.
  • The sum of the probabilities of all possible outcomes of a single event is always equal to 1.
  • Probability needs to be evaluated rationally, which means relying on the given situation and circumstances, as opposed to relying on personal intuition.

Complex Evaluations

  • In case of compound events, the total probability rule can be utilised to analyse probabilities. This rule states that for a set of mutually exclusive events, the sum of probabilities calculated by multiplying each event’s probability by the probability of the condition is equal to the total probability: **P(A) = ∑ P(A Bi) * P(Bi)**.
  • The complementary rule is used when it’s simpler to calculate the probability of the event not happening rather than the event itself. The rule states that the probability that event A happens is 1 minus the probability that it doesn’t happen: P(A) = 1 - P(A’).

Probability Distributions

  • Recognising the type of distribution in which the events are falling is a crucial step in evaluating probabilities accurately. The most common distributions to consider are binomial, uniform, normal and Poisson distributions, each of which has its own set of rules and formulas.
  • Understanding the properties of different distributions will offer structure in the approach towards complex probability evaluations.

By becoming familiar with these concepts and methodologies, one can accurately evaluate probabilities in diverse circumstances, which is a foundational skill in applied mathematics.