Probability in the context of "Punnett square"

In expected utility theory, a lottery is a discrete distribution of probability on a set of states of nature. The elements of a lottery correspond to the probabilities that each of the states of nature will occur, (e.g. Rain: 0.70, No Rain: 0.30). Much of the theoretical analysis of choice under uncertainty involves characterizing the available choices in terms of lotteries.

In economics, individuals are assumed to rank lotteries according to a rational system of preferences, although it is now accepted that people make irrational choices systematically. Behavioral economics studies what happens in markets in which some of the agents display human complications and limitations.

Justification (also called epistemic justification) is a property of beliefs that fulfill certain norms about what a person should believe. Epistemologists often identify justification as a component of knowledge distinguishing it from mere true opinion. They study the reasons why someone holds a belief. Epistemologists are concerned with various features of belief, which include the ideas of warrant (a proper justification for holding a belief), knowledge, rationality, and probability, among others.

Debates surrounding epistemic justification often involve the structure of justification, including whether there are foundational justified beliefs or whether mere coherence is sufficient for a system of beliefs to qualify as justified. Another major subject of debate is the sources of justification, which might include perceptual experience (the evidence of the senses), reason, and authoritative testimony, among others.

Pierre de Fermat (/fɜːrˈmɑː/; French: [pjɛʁ də fɛʁma]; 17 August 1601 – 12 January 1665) was a French magistrate, polymath, and above all mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' Arithmetica. He was also a lawyer at the parlement of Toulouse, France, a poet, a skilled Latinist, and a Hellenist.

This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantities and probabilities. Each number is given a name in the short scale, which is used in English-speaking countries, as well as a name in the long scale, which is used in some of the countries that do not have English as their national language.

The future is the time after the past and present. Its arrival is considered inevitable due to the existence of time and the laws of physics. Due to the apparent nature of reality and the unavoidability of the future, everything that currently exists and will exist can be categorized as either permanent, meaning that it will exist forever, or temporary, meaning that it will end. In the Occidental view, which uses a linear conception of time, the future is the portion of the projected timeline that is anticipated to occur. In special relativity, the future is considered absolute future, or the future light cone.

In the philosophy of time, presentism is the belief that only the present exists and the future and the past are unreal. Religions consider the future when they address issues such as karma, life after death, and eschatologies that study what the end of time and the end of the world will be. Religious figures such as prophets and diviners have claimed to see into the future.Future studies, or futurology, is the science, art, and practice of postulating possible futures. Modern practitioners stress the importance of alternative and plural futures, rather than one monolithic future, and the limitations of prediction and probability, versus the creation of possible and preferable futures. Predeterminism is the belief that the past, present, and future have been already decided.

Acatalepsy (from the Greek α̉- 'privative' and καταλαμβάνειν 'to seize'), in philosophy, is incomprehensibleness, or the impossibility of comprehending or conceiving some or all things. The doctrine held by the ancient Skeptic philosophers, that human knowledge never amounts to certainty, but only to probability.

The Pyrrhonians attempted to show, while Academic skeptics of the Platonic Academy asserted an absolute acatalepsia; all human science or knowledge, according to them, went no further than to appearances and verisimilitude. It is the antithesis of the Stoic doctrine of katalepsis or Apprehension. According to the Stoics, katalepsis was true perception, but to the Skeptics, all perceptions were acataleptic, i.e. bear no conformity to the objects perceived, or, if they did bear any conformity, it could never be known.

In probability theory and statistics, a probability distribution is a function that gives the probabilities of occurrence of possible events for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space).

For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.5 for X = tails (assuming that the coin is fair). More commonly, probability distributions are used to compare the relative occurrence of many different random values.

In common usage, randomness is the apparent or actual lack of definite patterns or predictability in information. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if there is a known probability distribution, the frequency of different outcomes over repeated events (or "trials") is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance, probability, and information entropy.

The fields of mathematics, probability, and statistics use formal definitions of randomness, typically assuming that there is some 'objective' probability distribution. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness.