Short answers, pulled from the story.
Probability is a number between 0 and 1 that describes how likely an event is to occur, where a larger number means the event is more likely. It is often expressed as a percentage from 0 percent to 100 percent, so a fair coin gives each side a probability of one half, written as 0.5 or 50 percent.
The word probability derives from the Latin probabilitas, which can also mean probity, a measure of the authority of a witness in a European legal case that was often correlated with the witness's nobility. Before the middle of the seventeenth century, the term probable meant approvable.
The doctrine of probabilities dates to the 1654 correspondence of Pierre de Fermat and Blaise Pascal, with earlier elementary work by Gerolamo Cardano. Christiaan Huygens gave the earliest known scientific treatment in 1657, and Andrey Kolmogorov developed the modern measure-theoretic theory in 1931.
Objectivists assign probability to describe an objective or physical state of affairs, with frequentist probability defining it as the relative frequency of an outcome when an experiment is repeated indefinitely. Subjectivists treat probability as a degree of belief, and the most popular subjective version is Bayesian probability, which combines expert knowledge with experimental data.
Probability theory is applied in risk assessment and modeling, with the insurance industry and markets using actuarial science to set pricing and trading decisions. It is also used to design games of chance so casinos make a guaranteed profit, to analyze trends in biology and ecology, and in reliability theory for consumer products like automobiles and electronics.
Probability theory is required to describe quantum phenomena because physical processes at sub-atomic scales have a random character governed by quantum mechanics. Under the Copenhagen interpretation, the wave function deals with probabilities of observing, resolved by a wave function collapse, though Albert Einstein objected with the remark that God does not play dice.