| combinations | groupings in which the order of members does not matter |
| compound event | an event with more than one outcome |
| conclusion | the part of a logical statement that provides the result or consequences of the hypothesis—In a statement “If x then y”, the conclusion is y. |
| conjecture | a statement that attempts to make a conclusion but has not been proved true or false |
| counterexample | a situation that provides evidence that a logical statement is false |
| counting numbers | also called natural numbers, the numbers 1, 2, 3, 4, ... |
| deductive reasoning | a form of logical thinking that uses generalizations to draw specific conclusions based on a series of logical steps, deductive reasoning may use rules, laws, and theories to support or justify a conjecture |
| dependent events | two or more events for which the occurrence of one affects the probability of the other(s) |
| equally likely | having the same likelihood of occurring, such that in a large number of trials, two equally likely outcomes would happen roughly the same number of times |
| event | a collection of possible outcomes, often describable using a common characteristic, such as rolling an even number with a die or picking a card from a specific suit |
| event space | the set of possible outcomes in an event: for example, the event “rolling an even number” on a die has the event space of 2, 4, and 6 |
| example | a situation that suggests a logical statement may be true |
| factorial | an abbreviated way of writing a product of all whole numbers from 1 to a given number, indicated by that number followed by an exclamation point, as in 3! = 3 • 2 • 1 |
| Fundamental Counting Principle | a way to find the number of outcomes in a sample space by finding the product of the number of outcomes for each element |
| generalize | the process of using observations of specific events to make statements or conjectures about more general situations |
| hypothesis | the part of a logical statement that provides the premise on which the conclusion is based—In a statement “If x then y,” the hypothesis is x. |
| independent events | two or more events for which the occurrence of one does not affect the probability of the other(s) |
| inductive reasoning | a form of logical thinking that makes general conclusions based on specific situations, inductive reasoning takes the path of observation to generalization to conjecture |
| integers | the numbers …, -3, -2, -1, 0, 1, 2, 3,… |
| irrational numbers | numbers between integers that cannot be written as a ratio of integers (that is, as |
| justify | provide a logical argument for a conclusion or conjecture |
| logical argument | a series of statements, each verifiable as true, that lead to a conclusion |
| logical statement | a statement that allows drawing a conclusion or result based on a hypothesis or premise |
| natural numbers | also called counting numbers, the numbers 1, 2, 3, 4, … |
| outcome | a result of a trial |
| overgeneralize | a logical mistake caused by basing a generalization on inadequate evidence or observation or by making too broad a conjecture, such as generalizing a pattern seen only in whole numbers to all real numbers |
| permutations | groupings in which the order of members matters |
| probability | a measure of how likely it is that something will occur |
| random | unable to be predicted with certainty |
| rational numbers | numbers that can be written as a ratio of integers (that is, as |
| real numbers | the set of numbers that includes both rational numbers and irrational numbers. |
| repeating decimals | numbers whose decimal parts repeat a pattern of one or more digits, these are all rational numbers |
| replacement | restoring a random situation back to its original state after performing an action |
| sample space | the set of all outcomes |
| simple event | an event with only one outcome |
| tree diagram | a diagram that shows the choices or random outcomes from multiple elements, using branches for each new element |
| trial | a random action or series of actions |
| whole numbers | the numbers 0, 1, 2, 3, …., or all natural numbers plus 0 |
where p and q are both integers), the decimal representation of an irrational number is non-repeating and non-terminating
where p and q are both integers and q ≠ 0)