Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. If an individual coin toss or the roll of dice is considered to be a random event, then if repeated many times the sequence of random events will exhibit certain patterns, which can be studied and predicted. Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem.
As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of large sets of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics.
A guitar pick is a plectrum used for guitars. A pick is generally made of one uniform material; examples include plastic, nylon, rubber, felt, tortoiseshell, wood, metal, glass, tagua and stone. They are often shaped in an acute isosceles triangle with the two equal corners rounded and the third corner rounded to a lesser extent.
Sports betting is the activity of predicting sports results and placing a wager on the outcome. It is generally considered to be a form of gambling.
The Pennsylvania Lottery is operated by the Commonwealth of Pennsylvania. The Lottery was created by the Pennsylvania General Assembly on August 26, 1971; two months later, Henry Kaplan was appointed as its first executive director. The Pennsylvania Lottery sold its first tickets on March 7, 1972 and drew its first numbers on March 15, 1972.
By Pennsylvania law, at least 40 percent of Lottery proceeds are required to be paid as prizes, with another 27 percent towards funding programs. Currently, the Pennsylvania Lottery exceeds these requirements, as 60.9 percent is paid as prizes, 29.9 percent to programs, 6.7 percent is paid as retailer and vendor commissions and 2.5 percent is consumed as operating expenses.
The Texas Lottery is the government-operated lottery available throughout Texas. It is operated by the Texas Lottery Commission, headquartered in downtown Austin.