Events
• A: the student received math class requested
,• B: the student is on the honor roll
To determine if all the students in her school have an equal opportunity to get into the math class requested is equivalent to determining that events A and B are independent.
If events A and B are independent, then:
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]From the data given in the table:
[tex]\begin{gathered} P(A\cap B)=\frac{125}{500} \\ P\mleft(A\mright)=\frac{340}{500} \\ P\mleft(B\mright)=\frac{205}{500} \end{gathered}[/tex]Substituting these values into the previous formula:
[tex]\begin{gathered} \frac{125}{500}=\frac{340}{500}\cdot\frac{205}{500} \\ \frac{125}{500}=\frac{69700}{250000} \\ 0.25\ne0.2788 \end{gathered}[/tex]Given that the formula is not satisfied, then the events are not independent. In consequence, the class assignment process is not fair