Although we typically do not have complete information about a population, we can use theorems and results from probability to arrive at statistical results. Underlying all of this is the assumption that we are dealing with random processes.This is why we stressed that the sampling procedure we used with the sock drawer was random.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.
For technical information on these subjects, Fermat and Pascal proposed somewhat different solutions, though they agreed about the numerical answer.
Each undertook to define a set of equal or symmetrical cases, then to answer the problem by comparing the number for .
Inherent in both probability and statistics is a population, consisting of every individual we are interested in studying, and a sample, consisting of the individuals that are selected from the population.
A problem in probability would start with us knowing everything about the composition of a population, and then would ask, “What is the likelihood that a selection, or sample, from the population, has certain characteristics?
This first round can now be treated as a fair game for this stake of 32 pistoles, so that each player has an expectation of 16.
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.Questions of this type would be: If instead, we have no knowledge about the types of socks in the drawer, then we enter into the realm of statistics.Statistics help us to infer properties about the population on the basis of a random sample.If we do not have a random sample, then we are no longer building upon assumptions that are present in probability.Our editors will review what you’ve submitted and determine whether to revise the article.Despite these practices and the common ground of the subjects, they are distinct.What is the difference between probability and statistics?It will never be known what would have happened had Cardano published in the 1520s.It cannot be assumed that probability theory would have taken off in the 16th century.” We can see the difference between probability and statistics by thinking about a drawer of socks. Depending upon our knowledge of the socks, we could have either a statistics problem or a probability problem.If we know that there are 30 red socks, 20 blue socks, and 50 black socks, then we can use probability to answer questions about the makeup of a random sample of these socks.