ISyE 8843 A , Brani Vidakovic Handout 1 1 Probability , Conditional Probability and Bayes Formula

The intuition of chance and probability develops at very early ages.1 However, a formal, precise definition of the probability is elusive. If the experiment can be repeated potentially infinitely many times, then the probability of an event can be defined through relative frequencies. For instance, if we rolled a die repeatedly, we could construct a frequency distribution table showing how many times each face came up. These frequencies (ni) can be expressed as proportions or relative frequencies by dividing them by the total number of tosses n : fi = ni/n. If we saw six dots showing on 107 out of 600 tosses, that face’s proportion or relative frequency is f6 = 107/600 = 0.178 As more tosses are made, we “expect” the proportion of sixes to stabilize around 16 .