Notice that there are no intersections between the different categories; for example, there are no students who would rather take an English class and a history class.
In general, if A and B are two independent events,
[tex]\begin{gathered} A,B\rightarrow\text{ independent events} \\ \Rightarrow P(A\cap B)=P(A)P(B) \end{gathered}[/tex]
In our case, for example, the probability of a student being male and choosing history is
[tex]\begin{gathered} P(Male\cap History)=\frac{10}{88} \\ while \\ P(Male)*P(History)=\frac{40}{88}*\frac{22}{88}=\frac{880}{88^2}=\frac{10}{88} \end{gathered}[/tex]
Thus, the events are independent.
The answer is 'This table is an example of the principle of independence. The first option.
