# Ch4_Outline - Chapter 4 Probability The Study of Randomness...

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Chapter 4: Probability – The Study of RandomnessI.Randomness (IPS section 4.1 pages 282-287)A. Random– We call a phenomenon random if individual outcomes are uncertain butthere is nonetheless a regular distribution of outcomes in a large number of repetitions. Random does NOT mean haphazard. It is a description of a kind of order that emerges only in the long run.B. Probability– The probability of any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of independent repetitions. That is, probability is long-term relative frequency.II.Probability Models (IPS section 4.2 pages 287-305)A.Sample Space– The sample space S of a random phenomenon is the set of all possible outcomes.B. Event – An event is an outcome or a set of outcomes of a random phenomenon. That is, an event is a subset of the sample space.C.Probability Rules:1.Any probability is a number between 0 and 1. 0 P(A) 12.All possible outcomes together must have probability 1. If S is the sample space in a probability model, then P(S) = 1.3. The probability that an event does not occur is 1 minus the probability that the event does occur. The complement of any event A is the event that A does not occur, written as Ac. The complement rulestates that P(Ac) = 1 – P(A)4.If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities. Two events A and B aredisjointif they have no outcomes in common and so can never occur simultaneously. If A and B are disjoint, P(A or B) = P(A) + P(B)