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I think it means to find the theoretical probability of something random that has results that are numbers. For instance, rolling a die and trying to get a 6 is a "chance activity with numerical outcomes".
That there is a 99% chance that the results of the brewer's study happened because of his manipulation of the IV and not by chance
A forecast that says, for instance, "there is a 10% chance of rain tomorrow," means that on 10 out of 100 days with weather conditions very similar to the conditions expected tomorrow, at least a trace of train has occurred. Some will disagree with this answer for various reasons. For the results of research that evaluated how understanding of percentage chance of precipitation varies around the world, see "A 30% Chance of Rain Tomorrow: How Does the Public Understand Probabilistic Weather Forecasts?," available as a PDF file via the URL http://www.mpib-berlin.mpg.de/en/mitarbeiter/gigerenzer/pdfs/RainFinal.pdf .
Statistics is used all the time in science and technology. In short, statistics tell us whether our results are probably caused by chance or not. Statistics is used in research to compare results between different treatments. It can also help describe relationships between variables and results over time. The most important thing is that it tells you when your differences are large enough to probably not be caused by chance. Statistics can also used in manufacturing by setting specification ranges and other quality attributes.
These errors occur due to chance. These errors tend to cancel to each other in long run. These errors are random. They are not the results of any prejudice or bais.