Ap Stat: Probability: The Study Of Randomness

AP Stat Chapter 6 Probability: The study of Randomness By Andrew Staniforth Random Phenomena – outcomes we cant predict but nonetheless have a regular distribution in very many repetitions Probability – is the proportion of items the event occurs in many repeated trials of a random phenomenon Probability model – for random phenomenon consists of a sample space S and an assignment of probabilities P Sample Space S – set of all possible outcomes of the random phenomenon Assignment of Probability – assigned a number P(A) to an event A as its probability Complement (Ac ) of an event A consists of exactly the outcomes that are not in A. Disjoint – if A and B have no outcomes in common Independent – if one event occurring does not change the probability we would assign to the other event Event – an outcome or a set of outcomes of a random phenomenon. That is, an event is a subset of the sample space. Tree Diagram

Rules for Assignment 0<=P(A)<=1 for any event A P(S)=1 Complement rule: For any event A, P(Ac)=1-P(A) Addition Rule – If events A and B are disjoint, then P(A or B) = P(A) + P(B) Multiplication rule – If events A and B are independent, then P(A and B) = P(A)P(B) General Addition Rule for Unions of Two Events - P(A or B) = P(A) + P(B) – P(A and B) General Multiplication rule – P (A and B) = P(A)∙P (B│A) Conditional Probability – P (B│A) = P (A and B) / P(A) Disjoint – P (A and B) = 0 Independent: P (A) = P(A│B) Venn Diagram:

Tree Diagram: