Event-outcome chance {probability} {risk} is between zero and one. To find probability, count how many times outcome happens compared to how many times event repeats: p = outcomes / events. Probability can be from theory {a priori probability} or from experiment {empirical probability}.
First-event outcome can influence second-event outcome {conditional probability}| {prior probability}. For conditional probability, to find probability that outcome happens in first event and outcome happens in second event, multiply first-outcome probability times modified second-outcome probability {conditional probability law} {law of conditional probability}: P = p1 * p2(p1).
Systematic probability {Kolmogorov probability} {Kolmogorov axioms} can use three axioms. Outcome probability is zero or positive real number. Probability that event has some outcome is one. For disjoint subsets, probability of union of subsets is sum of subset probabilities {sigma-additivity} {additivity}.
The more times event repeats, the closer to actual probability outcome-probability becomes {large numbers law} {law of large numbers}.
People can believe that an improbable situation that has not happened recently is more likely to happen now, or that the past affects next outcome of random process {Monte Carlo fallacy} {gambler's fallacy}.
Expected outcome divided by outcome value measures risk {risk, outcome}. Expected outcome value is worth or gain multiplied by probability.
After many independent events, relative frequency approaches outcome probability {weak law of large numbers}.
Probability is 0.5 that at least two people out of 25 have same birthday {birthday, probability}.
What is probability that needle falls on parallel lines {Buffon's problem} {Buffon problem}? Probability that needle touches line is 2 * l / (pi * d), where l is needle length and d is distance between lines.
First, contestant chooses one of three outcomes. Then contestant learns that one of other two outcomes is incorrect. Do people switch to another outcome or keep current choice {Monty Hall problem}? Switch, because first guess was only 1/3 correct, but second guess must be 2/3 correct, because contestant now knows that probability of one outcome is zero.
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0225