Study of probability theory and probability models for dice game of craps

Abstract

Probability is the language of uncertainty. Using statistics, we can better predict the outcomes of random phenomena over the long term – from the very complex, like weather, to the very simple, like a coin flip, or of more interest to gamblers, a dice toss. A probability is a numerical value assigned to a given event A. The probability of an event is written P(A), and describes the long-run relative frequency of the event. The first two basic rules of probability are the following: Rule 1: Any probability P(A) is a number between 0 and 1 (0 < P(A) < 1). Rule 2: The probability of the sample space S is equal to 1 (P(S) = 1). The sample space S for a probability model is the set of all possible outcomes. An event A is a subset of the sample space S.