In order to calculate the probability of a student from this sample to be a seventh grader, we need to divide the number of seventh graders by the total number of students. This is done below:
[tex]\begin{gathered} P(\text{seventh grader)}=\frac{4}{10+4+6} \\ P(\text{seventh grader)}=\frac{4}{20} \\ P(\text{seventh grader)}=\frac{1}{5} \end{gathered}[/tex]A. The probability of a random selected student being a seventh grader is 1/5.
In order to calculate the probability of the selected student not being a seventh grader, we need to subtract the probability of them being a seven grader from one, because these two events are mutually exclusive. So we have:
[tex]\begin{gathered} P(\text{not seventh grader)}=1-\frac{1}{5} \\ P(\text{not seventh grader)}=\frac{5}{5}-\frac{1}{5} \\ P(\text{not seventh grader)}=\frac{4}{5} \end{gathered}[/tex]B. The probability of a random selected student not being a seventh grader is 4/5.
