Review Vocabulary

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Addition rule (general) The probability that one event or the other occurs is the sum of their individual probabilities minus the probability of any overlap they have. (p. 351)

Central limit theorem The average of many independent random outcomes is approximately normally distributed. When we average independent repetitions of the same random phenomenon, the resulting distribution of outcomes has mean equal to the mean outcome of a single trial and standard deviation equal to times the standard deviation of a single trial. (p. 380)

Combination An unordered collection of items chosen (without allowing repetition) from a set of distinct items. (p. 367)

Combinatorics The branch of mathematics that studies how to count and choose elements. (p. 363)

Complement of an event The complement of an event is the event “ does not occur,” which is denoted . (p. 350)

Complement rule The probability that an event does not occur is 1 minus the probability that the event does occur: . (p. 350)

Conditional probability Written as , this can be computed by dividing the probability that both events occur by the probability that occurs. (pp. p. 356 p. 357)

Continuous probability model A probability model that assigns probabilities to events as areas under a density curve. (p. 372)

Density curve A curve that is always on or above the horizontal axis and has area exactly 1 underneath it. A density curve describes a continuous probability model. (pp. p. 371 p. 372)

Discrete probability model A probability model that assigns probabilities to each of a countable number of possible outcomes. (p. 361)

Disjoint (mutually exclusive) events Events that have no outcomes in common. (p. 350)

Event A collection of possible outcomes of a random phenomenon; a subset of the sample space. (p. 346)

Factorial The product of the first positive integers is factorial, denoted as ! (pp. p. 365 p. 366)

Fundamental principle of counting A multiplicative method for counting outcomes of multistage processes. (p. 363)

Independent events Events that do not influence each other’s probability of occurring. Two events and are independent if . (p. 354)

Law of large numbers As a random phenomenon is repeated many times, the mean of the observed outcomes approaches the mean of the probability model. (p. 378)

Mean of a discrete probability model The average outcome of a random phenomenon with numerical values. When possible values have probabilities , the mean is the average of the outcomes weighted by their probabilities, . Also called expected value. (p. 375)

Multiplication rule for independent events If two events are independent, then the probability that one event and the other both occur is the product of their individual probabilities: , when and are independent events. (p. 356)

Permutation An ordered arrangement of items chosen (without allowing repetition) from a set of distinct items. (pp. p. 364 p. 365)

Probability A number between 0 and 1 that gives the long-run proportion of repetitions of a random phenomenon on which an event will occur. (pp. p. 343 p. 344)

Probability histogram A histogram that displays a discrete probability model when the outcomes are numerical. The height of each bar is the probability of the event at the base of the bar. (p. 353)

Probability model A sample space together with an assignment of probabilities to events. The two main types of probability models are discrete and continuous. (pp. p. 345 p. 346)

Random A phenomenon or trial is random if it is uncertain what the next outcome will be, but each outcome nonetheless tends to occur in a fixed proportion of a very long sequence of repetitions. These long-run proportions are the probabilities of the outcomes. (p. 343)

Sample space The set of all possible (simplest) outcomes of a random phenomenon. If the outcomes in a sample space can be listed, the sample space is discrete. (p. 345)

Standard deviation of a discrete probability model A measure of the variability of a probability model. When the possible values have probabilities the standard deviation is the square root of the average (weighted by probabilities) of the squared deviations from the mean:

(p. 379)