Probability Rules and Axioms
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Probability is a way to quantify the uncertainty that arises from conducting experiments using a random sample from the population of interest. Probability of an event happening = (Number of ways it can happen) / (Total number of outcomes)
Example: the chances of rolling a '3' with a die Number of ways it can happen: 1 Total number of outcomes: 6 So the Probability = 1/6
Sample Space: all the possible outcomes of an experiment Sample Point: just one of the possible outcomes Event: one or more outcomes of an experiment
Example: the chances of a "double" when rolling 2 dice. Sample Space: Possible outcomes. 36 sample points {1,1} {1,2} {1,3} {1,4} ... {6,3} {6,4} {6,5} {6,6}
Event: Looking for double. Event is made up of 6 sample points. {1,1} {2,2} {3,3} {4,4} {5,5} and {6,6} Run 100 Experiments, and find how many Events you observe.
Probability Rule One: For any event A, 0 ≤ P(A) ≤ 1 Probability Rule Two: The sum of the probabilities of all possible outcomes is 1. Probability Rule Three: P(not A) = 1 – P(A) Probability Rule Four: If A and B are disjoint events, then P(A or B) = P(A) + P(B)
Axiom One: The probability of an event is a non-negative real number that is greater than or equal to 0. Axiom Two: The probability of the entire sample space is one(no events exist outside of the sample space) Axiom Three: If two events A and B are mutually exclusive, then the probability of either A or B [i.e P(A U B)] = P(A) + P(B)
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