# CHAPTER 3RANDOM ERROR THEORY

## 3.1 INTRODUCTION

As noted earlier, the adjustment of measured quantities containing random errors is a major concern to people involved in the geospatial sciences. In the remaining chapters, it is assumed that all systematic errors have been removed from the observed values and that only random error and blunders, which have escaped detection, remain. In this chapter the general theory of random errors is developed, and some simple methods that can be used to isolate blunders in sets of data are discussed.

## 3.2 THEORY OF PROBABILITY

*Probability* is the ratio of the number of times that an event should occur to the total number of possibilities. For example, the probability of tossing a two with a fair die is 1/6 since there are six total possibilities (faces on a die) and only one of these is a two. When an event can occur in *m* ways and fail to occur in *n* ways, then the probability of its occurrence is *m*/(*m* + *n*) and the probability of its failure is *n*/(*m* + *n*).

Probability is always a fraction ranging between zero and 1. Zero denotes impossibility and one indicates certainty. Since an event must either occur or fail to occur, the sum of all probabilities for any event is 1, and thus if 1/6 is the probability of throwing a two with one throw of a die, then 1 – 1/6, or 5/6 is the probability that a two will not appear.

In probability terminology, a ...

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