Probability (P): The chance of occurrence of a particular event.
Experiment : An experiment is an operation which can produce well-defined outcomes.
Random Experiment : The experiment when all possible outcomes of an experiment are known but exact outcome cannot be predicted in advance.
E.g. Tossing fair coin, rolling an unbiased dice and drawing a card from a pack of shuffled cards.
Sample Space (S): The set of all possible outcomes of an experiment and denoted by S.
Eg. When coin tossed, S = {H, T} where H = Head and T = Tail
Event (E): Any subset of a sample space.
Probability of occurrence of an Event :
E ⊆ S
P(E) = n(E)/n(S)
Results on Probability :
  • P(S) = 1
  • 0 ≤ P(E) ≤ 1
  • P(ϕ) = 0
  • For any events A and B we have : P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
  • If A denotes (not-A), then P(A) = 1 - P(A).