You have a fair 6 sided dice. What is the probability that the roll will be prime?[br]Let E be the event that the dice is rolled is prime. We are trying to find P(E).[br]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)=
1/2 [br]Since the number of outcomes in E is 3 and the number of outcomes in the sample space [math]\Omega[/math] is 6.[br] [math]\frac{\left|\left\{2,3,5\right\}\right|}{\left|\left\{1,2,3,4,5,6\right\}\right|}=\frac{3}{6}[/math][br]
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4
Classical Method
The classic method for finding probabilities is only used when each outcome is equally likely.[br]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.[br]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[br][math]P\left(E\right)=\frac{\left|E\right|}{\left|\Omega\right|}[/math]
Other Theoretical Methods
Later we will use Venn diagrams and the fact that P(Ω) = 1 to find probabilities.[br]We will also be using tree diagrams for finding probabilities when chance outcomes have intermediate stages or can be broken into discrete categories.[br]We will also learn the addition and product rule to find probabilities.[br]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.