QMB 3200 UCF CHAPTER 4 QUESTIONS AND ANSWERS 2024

Addition law A probability law used to compute the probability of the union of two events. It is P(A ∩ B) = P(A) + P(B) − P(A ∪ B). For mutually exclusive events, P(A ∩ B) = 0; in this case the addition law reduces to P(A ∪ B) = P(A) + P(B). Basic requirements for assigning probabilities Bayes’ theorem A method used to compute posterior probabilities. Classical method A method of assigning probabilities that is appropriate when all the experimental outcomes are equally likely. Combination Complement of A The event consisting of all sample points that are not in A. Conditional probability Event A collection of sample points. Experiment A process that generates well-defined outcomes. Independent events Two events A and B where P(A | B) = P(A) or P(B | A) = P(B); that is, the events have no influence on each other. Intersection of A and B he event containing the sample points belonging to both A and B. The intersection is denoted A ∩ B. Joint probability The probability of two events both occurring; that is, the probability of the intersection of two events. Marginal probability The values in the margins of a joint probability table that provide the probabilities of each event separately. Multiple-step experiment Multiplication law A probability law used to compute the probability of the intersection of two events. It is P(A ∩ B) = P(B)P(A | B) or P(A ∩ B) = P(A)P(B | A). For independent events it reduces to P(A ∩ B) = P(A)P(B). Mutually exclusive events Events that have no sample points in common; that is, A ∩ B is empty and P(A ∩ B) = 0. Permutation Posterior probabilities Revised probabilities of events based on additional information. Prior probabilities Initial estimates of the probabilities of events. Probability A numerical measure of the likelihood that an event will occur. Relative frequency method A method of assigning probabilities that is appropriate when data are available to estimate the proportion of the time the experimental outcome will occur if the experiment is repeated a large number of times. Sample point An element of the sample space. A sample point represents an experimental outcome. Sample space The set of all experimental outcomes. Subjective method A method of assigning probabilities on the basis of judgment. Tree diagram A graphical representation that helps in visualizing a multiple-step experiment. Union of A and B The event containing all sample points belonging to A or B or both. The union is denoted A ∪ B. Venn diagram A graphical representation for showing symbolically the sample space and operations involving events in which the sample space is represented by a rectangle and events are represented as circles within the sample space.