Probability of an elementary events

In the presumed knowledge section we considered the idea that when we look at an experimental situation we find answers that indicate that a theoretical application is appropriate. This theoretical approach is called probability and is what we will explore in this chapter. Consider a number of equally likely outcomes of an event. What is the probability of one specific outcome of that event? For example, if we have a cubical die what is the probability of throwing a six?

Since there are six equally likely outcomes and only one of them is throwing a six, then the probability of throwing a six is 1 in 6. We would normally write this as a fraction or as a decimal or a percentage. Since probability is a theoretical concept, it does not mean that if we throw a die six times we will definitely get a six on one of the throws.

However, as the number of trials increases, the number of sixes becomes closer to of the total.

Generally, if the probability space S consists of a finite number of equally likely outcomes, then the probability of an event E, written P(E) is defined as:

where n(E) is the number of occurrences of the event E and n(S) is the total number of possible outcomes.

Hence in a room of fifteen people, if seven of them have blue eyes, then the probability that a person picked at random will have blue eyes is

where P(A’) is the probability that the event A does not occur.

A’ is known as the complement of A.

where P(A’) is the probability that the event A does not occur.