Probability is especially important in statistics because of the many principles and procedures based upon this concept. Indeed, probability plays a special role in all our lives, because we use it to measure uncertainty. We are continually faced with decisions leading to uncertain outcomes, and we rely on probability to help us make our choice. Think of the planned outdoor activities, such as picnics or boating, you canceled because the chance of bad weather seemed too likely. Remember those nights before examinations when you decided not to study some topics, because they probably would not be covered on the test?

A probability is a numerical value that measures the uncertainty that a particular event will occur. The probability of an event ordinarily represents the proportion of times under identical circumstances that the outcome can be expected to occur. We refer to this value as the event’s long-run frequency of occurrence. The probability that the head side will slow when a fair coin is tossed is 1/2. This can be verified experimentally by tossing a coin several times and observing that “heads” occur about one-half of those times.Probability is a necessary part of statistical inference, because it measures the uncertainties involved in making generalizations from a sample. Suppose that 10,000 men are selected at random from adult American males. If we know exactly how many seven-footers there are in the populations, we may calculate the probability that our sample will contain any number of men taller than seven feet.

But records of the heights of all American men are not available, so the actual number of seven-footers remain unknown. If, how ever, the number of seven-footers in the sample is counted, then the number in the populations may be estimated from the sample. But the accuracy of this estimate will remain uncertain. Common sense tells us that it would be unlikely for the sample to differ substantially from the population, so that the proportion of very tall men may be expected to be roughly the same. Probability is required to indicate just how likely the sample is to yield estimates that are in error by various amounts.

Probability was initially studied scientifically by several famous mathematicians more than 300 years ago in connection with gambling problems. The theory of probability has since evolved into one of the most elegant and useful branches of mathematics. Today devices ordinarily associated with gambling, such as dice and playing cards, are still useful in illustrating how to find probabilities