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Properties of Probabilities

1.2 Introduction to Probabilities

Probabilities

  • Probability is a numerical measure of the chance of a particular event occurring.
  • It is defined that the sum of probabilities of all possible outcomes to be 1, and all individual probabilities is non-negative. To sum up, the probability of each outcome is a real number in the interval [0,\ 1].
  • The probability of an event is equal to the sum of the probabilities of the outcomes in that event.
  • Mathematically, we represent probability of an event as \operatorname{Pr}(X=x) or \operatorname{Pr}(x), which X is the criteria to be observed, and x is the (actual) possible outcome.
  • Usually, we assume that each outcome is equally likely to happen i.e. have the same probability, unless there are conditions/evidence that says otherwise. Thus, if there are n equally likely outcomes, probability of each event is \frac{1}{n}.
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