This is a problem in my text that I have the solution for. I do not understand how the solution is achieved however. I was hoping someone could enlighten me on the reasoning behind this. I took statistics nearly two years ago and it's faded some.

Problem:A disadvantage of a broadcast subnet is the capacity wasted when multiple hosts attempt to access the channel at the same time. As a simplistic example, suppose that time is divided into discrete slots, with each of thenhosts attempting to use the channel with probabilitypduring each slot. What fraction of the slots will be wasted due to collisions?

Solution from text:Distinguishn+ 2 events. Events 1 throughnconsist of the corresponding host successfully attempting to use the channel, i.e., without a collision. The probability of each of these events is:

$\displaystyle p(1-p)^{n-1}$

Eventn+ 1 is an idle channel, with probability

$\displaystyle (1-p)^n$

Eventn+ 2 is a collision. Since thesen+ 2 events are exhaustive, their probabilities must sum to unity. The probability of a collision, which is equal to the fraction of slots wasted, is then just

$\displaystyle 1-np(1-p)^{n-1}-(1-p)^n$.