Section 43 Probability: Terminologies

43.1 Explanation of terms

• Experiment
  • An experiment or trial is any procedure that can be infinitely repeated
  • It has a well-defined set of possible outcomes for each occasion
  • An experiment is generally repeated in identical conditions
  • A fixed number of repetitions of the same experiment can be thought of as a composed experiment, in which case the individual repetitions are called trials

• Outcome
  • An outcome is a possible result of an experiment

• Random experiment
  • An experiment that results more than one outcome

• Sample space
  • The set of all possible outcomes of a random experiment is called the sample space of the experiment.
  • The sample space is denoted as S.
  • A sample space is discrete if it consists of a finite or countable infinite set of outcomes.
  • A sample space is continuous if it contains an interval (either finite or infinite) of real numbers.

• Event
  • An event is a set of outcomes of a random experiment.
  • It is a subset of the sample space to which a probability is assigned.

• Probability

  • Probability is the measure of the likelihood that an event will occur.
  • The probability of an Event is the number of ways the event occurs in a random experiment (n) divided by the total number of possible outcomes in a random experiment (N)

  \[ \large Prob(Event) = \frac{n}{N} \]

  • Probabilities can be written as fractions, decimals or percentages.
  • In faction, it ranges from 0 to 1; starting at 0 (impossible) and ending at 1 (certain).
  • The sum of the probabilities of all possible outcomes is 1