advertisement

© Jill Zarestky Math 141 Week in Review Week in Review 6 Key Topics 7.1 Experiments, Sample Spaces, and Events An experiment is an activity with an observable result. • The result of the experiment is called the outcome or sample point. • The set of all outcomes or sample points is called the sample space of the experiment. o A sample space may be finite, in which case you can list all the elements. o An infinite sample space has to be described and you can't list all the elements. o A uniform sample space has equally likely outcomes. • An event is a subset of a sample space. Mutually Exclusive • Events E and F are mutually exclusive if E ∩ F = ∅, that is, if E and F are disjoint. 7.2 Definition of Probability Empirical Probability • An estimate of the probability of an event based upon how often the event occurs after collecting data or running an experiment with many trials. • If the relative frequency approaches some value P(E) as the number of experiments n increases, then P(E) is said to be the empirical probability. Theoretical Probability • Based on the sample space having equally likely outcomes. • Find probability by using a sample space of equally likely outcomes. • The probability of an event, P(E) is a number between 0 and 1. o An event with probability 0 is impossible and an event with probability of 1 is certain to occur. Simple Events • {s1}, {s2} . . . {sn} for a uniform sample space S = {s1, s 2, ..., sn} • Simple events are mutually exclusive because only one can occur at a time. • Then the probability of each of the simple events is P(s 1) = P(s2) = . . . = P(sn) = • 1 n . The probability of each simple event is the same. Probability Distribution • Probability is assigned to each event. • If S is the finite sample space of an experiment with n outcomes where each of the simple events are mutually exclusive from each other, then 1. 0 ≤ P(si) ≤ 1 2. P(s1) + P(s2) + . . . + P(sn) = 1 3. P({si} ∪ {sj}) = P(si) + P(sj) 1 © Jill Zarestky Math 141 Week in Review 7.3 Rules of Probability Properties of the Probability Function • P(E) ≥ 0 for any E • P(S) = 1 • If E and F are mutually exclusive, P(E ∪ F) = P(E) + P(F) • If E and F are any two events of an experiment, P(E ∪ F) = P(E) + P(F) – P(E ∩ F) • P(EC) = 1 – P(E) 2