Probability
Concept 5.1 Probability Rules
Probability is a measure of likelihood of a random phenomenon or chance behavior occurring. Probability describes the long-term proportion with which a certain outcome will occur in situations with short-term uncertainty.
Probability deals with experiments which yield random short-term results or outcome.
Experiment → Any process that can be repeated, in which results are uncertain.
Sample Space (S) → Collection of all possible outcomes.
Event → Any collection of outcomes from a probability outcome.
Simple Events (e i) → events with one outcome.
Probability Model: Lists the possible outcomes of a probability experiment and each outcome’s probability and must satisfy rules 1 and 2.
If an event is impossible, the probability of the event is 0.
If an event is certain, the probability of the event is 1.
If an event is unusual, it has a low probability of occurring.
Classical Method Rules/Expectations
Classical method of computing probability requires equally likely outcomes.
An experiment is said to have equally likely outcomes when each simple event has the same probability of occurring.
If an experiment has n equally likely outcomes and if the # of ways that an event E can occur is m, then the probability of E, P(E) is:
P(E) = # of ways E can occur / # of outcomes in sample space.
Law of Large Numbers
As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the outcome.
Rules of Probabilities
Probability of any event E, P(E) must be greater than or equal to 0 and less than or equal to 1. That is, 0 <= P(E) <= 1;
Sum of the probabilities must equal 1. That is, if sample space:
S ={e1, e2, …, en}, then P(e1) + P(e2)