Probability Theory, 2nd Edition

7 Limit theorems

Probability Theory does not have the ability to predict the occurrence or nonoccurrence of a single event in a random experiment; besides, this event occurs either with probability one or with probability zero. For example, Probability Theory does not give any information about the next result when rolling a die, it does not predict the numbers appearing next week on the lottery nor is it able to foresee the lifetime of a component in a machine. Such statements are impossible within the theory. The theory is only able to say that some events are more likely and others are less likely. For instance, when rolling a die twice, it is more likely that the sum of both rolls will be “7” than “2.” Nevertheless, next when we roll ...