What are the basics of probability?

Probability Basics

Probability is a fundamental concept in mathematics that measures the likelihood of an event occurring. It's expressed as a value between 0 (impossible) and 1 (certain). Here are the basics of probability:

  • Random Event: An event that may or may not occur under certain conditions is called a random event. The outcome of such an event is uncertain.

  • Experiment/Trial: A random event that can be repeated under the same conditions is called an experiment or trial. Each repetition is called a trial.

  • Sample Space: The set of all possible outcomes of an experiment is called the sample space, often denoted by the symbol S.

  • Event: A subset of the sample space is called an event, denoted by the symbol E. It's a specific outcome or set of outcomes that we're interested in.

  • Probability of an Event: The probability of an event E, denoted by P(E), is the measure of the likelihood that E will occur. It's calculated as the ratio of the number of favorable outcomes (n(E)) to the total number of possible outcomes (n(S)), or P(E) = n(E) / n(S).

  • Basic Properties of Probability:

    • The probability of an impossible event is 0.
    • The probability of a certain event is 1.
    • The probability of the entire sample space is 1.
What are the basics of probability? — Probability Basics | Unlo