TABLE OF CONTENTS This chapter deals with distributions which model many real-life situations. We assume a series of trials where there are two possible outcomes per trial and the probability for each outcome is the same for all trials. We also assume that outcomes of different trials are independent events. Applications abound in law, medicine, political science, sports, and other areas.
The following example is identical to Example 5.2 except that sampling is carried out with replacement.
Example 6.1. A box contains eight red and six white chips. Four chips are drawn with replacement from the box. Let X denote the number of red chips drawn. Find an expression for the probabilities of the following events:
Three red chips followed by one white chip.
One red chip followed by one white chip and then two red chips.
X = 3
X ? 3
Solution:
since the numbers of terms in the sum equals the number of words with 3 R s, 1 W which is 
.
.
The difference between this model and the one used in Example 5.2 is that we have independence from draw to draw here since we are sampling with replacement. So events such as red chip on first draw and red chip on second draw are independent events.
In terms of an experiment where chips are drawn from a box, the binomial model satisfies three conditions:
Two types of chips in the box.
