Classical Method to Determine Probability
A Classic Example
You have a fair 6 sided dice. What is the probability that the roll will be prime?
Let E be the event that the dice is rolled is prime. We are trying to find P(E).
Each outcome in the sample space is equally likely so we can take the number of outcomes in E and divide it by the number of outcomes in the entire sample space to find P(E).
P(E)=
Notation. | { } |
Mathematicians often use absolute value vertical bars to denote the number of elements in a set.
Find |{blue,red,green,yellow}|.
Classical Method
The classic method for finding probabilities is only used when each outcome is equally likely.
To find the probability of an event E, take the number of outcomes in E and divide it by the total number of outcomes in the sample space.
Since an event can be considered the set of all outcomes it comprises we can write the classical method for finding the probability of event E as
Other Theoretical Methods
Later we will use Venn diagrams and the fact that P(Ω) = 1 to find probabilities.
We will also be using tree diagrams for finding probabilities when chance outcomes have intermediate stages or can be broken into discrete categories.
We will also learn the addition and product rule to find probabilities.
Sometimes the only way to find probability is by guess work and intuition, but you won't be asked to do that on a test.