NSES Content Standard Unifying Concepts and Processes:   Systems, order, and organization  Grades K-12, page 117  Order--the behavior of units of matter, objects, organisms, or events in the universe--can be described statistically. Probability is the relative certainty (or uncertainty) that individuals can assign to selected events happening (or not happening) in a specified space or time. In science, reduction of uncertainty occurs through such processes as the development of knowledge about factors influencing objects, organisms, systems, or events; better and more observations; and better explanatory models.

Benchmark 4E The Physical Setting: Energy Transformations
Grades 9-12, page 86
Heat energy in a material consists of the disordered motions of its atoms or molecules. In any interactions of atoms or molecules, the statistical odds are that they will end up with less order than they began--that is, with the heat energy spread out more evenly. With huge numbers of atoms and molecules, the greater disorder is almost certain.

Benchmark 9D The Mathematical World: Uncertainty
Grades 6-8, page 229
How probability is estimated depends on what is known about the situation. Estimates can be based on data from similar conditions in the past or on the assumption that all the possibilities are known.

Benchmark 9D The Mathematical World: Uncertainty
Grade 6, page 229
Probabilities are ratios and can be expressed as fractions, percentages, or odds.

Benchmark 9D The Mathematical World: Uncertainty
Grade 6, page 229
The larger a well-chosen sample is, the more accurately it is likely to represent the whole. But there are many ways of choosing a sample that can make it unrepresentative of the whole.

Benchmark 9D The Mathematical World: Uncertainty
Grade 9, page 230
Even when there are plentiful data, it may not be obvious what mathematical model to use to make predictions from them or there may be insufficient computing power to use some models.

Benchmark 9D The Mathematical World: Uncertainty
Grade 9, page 230
A physical or mathematical model can be used to estimate the probability of real-world events.

Benchmark 11C Common Themes: Constancy and Change
Grades 9-12, page 275
Most systems above the molecular level involve so many parts and forces and are so sensitive to tiny differences in conditions that their precise behavior is unpredictable, even if all the rules for change are known. Predictable or not, the precise future of a system is not completely determined by its present state and circumstances but also depends on the fundamentally uncertain outcomes of events on the atomic scale.

Science for All Americans The Mathematical World
Chapter 9, page 135
Our knowledge of how the world works is limited by at least five kinds of uncertainty: (1) inadequate knowledge of all the factors that may influence something, (2) inadequate number of observations of those factors, (3) lack of precision in the observations, (4) lack of appropriate models to combine all the information meaningfully, and (5) inadequate ability to compute from the models. It is possible to predict some events with great accuracy (eclipses), others with fair accuracy (elections), and some with very little certainty (earthquakes). Although absolute certainty is often impossible to attain, we can often estimate the likelihood--whether large or small--that some things will happen and what the likely margin of error of the estimate will be.