Introduction to Probability

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Introduction to Probability

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Presentation transcript:

Introduction to Probability Basic ideas and concepts

What is Probability? For a random phenomenon, individual outcomes are not certain but there is a regular distribution of outcomes in the long run. The probability of an outcome is its long-term relative frequency.

What are the possible outcomes? We want to make a list of possible outcomes, then find the probability for each outcome. The sample space is the set of all possible outcomes. Events are specific outcomes or a set of outcomes in the sample space.

Useful facts about probability The probability of an event cannot be less than 0 or greater than 1. All possible outcomes together must have probability 1. The probability of an event occurring is 1 minus the probability that it does not occur. If 2 events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities

Useful facts about probability The events A and B are said to be independent if the occurrence of A does not affect the probability that B occurs, and vice versa. Thus, for independent events A and B, P(AB) = P(A)·P(B)