# Probability For Statistics

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The Event Alex is looking for is a "double", where both dice have the same number.

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Statistics may be said to have its origin in census counts taken thousands of years ago; as a distinct scientific discipline, however, it was developed in the early 19th century as the study of populations, economies, and moral actions and later in that century as the mathematical tool for analyzing such numbers.

For technical information on these subjects, Fermat and Pascal proposed somewhat different solutions, though they agreed about the numerical answer.

Fermat and Pascal were not the first to give mathematical solutions to problems such as these.

More than a century earlier, the Italian mathematician, physician, and gambler Girolamo Cardano calculated odds for games of luck by counting up equally probable cases.Hence Games of chance such as this one provided model problems for the theory of chances during its early period, and indeed they remain staples of the textbooks.A posthumous work of 1665 by Pascal on the “arithmetic triangle” now linked to his name ( binomial theorem) showed how to calculate numbers of combinations and how to group them to solve elementary gambling problems.It may be defined as the proportion of favourable outcomes to the total number of possibilities if these are indifferent (mathematical probability), or the proportion observed in a sample (empirical probability), or the limit of this as the sample size tends to infinity (relative frequency), or by more subjective criteria (subjective probability) A number expressing the likelihood of the occurrence of a given event, especially a fraction expressing how many times the event will happen in a given number of tests or experiments. Many events can't be predicted with total certainty.He reasoned that two more games would suffice in any case to determine a victory.There are four possible outcomes, each equally likely in a fair game of chance.Producing Data: This unit is organized into two sections – Sampling and Designing Studies.Probability: In this course the unit is a classical treatment of probability and includes basic probability principles, finding probability of events, conditional probability, discrete random variables (including the Binomial distribution) and continuous random variables (with emphasis on the normal distribution).The probability unit culminates in a discussion of sampling distributions that is grounded in simulation.For a streamlined version of probability that forgoes the classical treatment of probability in favor of an empirical approach using relative frequency, participants may see the OLI Statistical Reasoning course.

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