Analysis of Ability for Understanding the Basic Concepts of Probability Theory

Suppose we run an experiment like throwing a die a number of times. Sometimes six dots show up on the top face, but more often fewer than six dots show up. We refer to six dots appearing at the top face as event A. Common sense tells us that the probability of event A occurring is 1/6, because every face is equally likely to appear at the top after a throw. The probability of event A is defined as the ratio of the number of times A occurs to the total number of outcomes. We call an experiment a procedure that yields one of a given set of possible outcomes. The sample space, denoted S, of the experiment is the set of possible outcomes. An event A is a subset of the sample space. Laplace’s definition of probability of an event A is