The probability of an event is obtained as follows:
[tex]Pr(\text{Event)}=\frac{number\text{ of favourable outcomes}}{number\text{ of sample space}}[/tex][tex]\begin{gathered} Pr(a\text{ student earns a grade of A) = }\frac{number\text{ of students that earn grade A}}{Total\text{ number of students}} \\ Pr(a\text{ student earns a grade of A)=}\frac{5}{35} \\ \\ Pr(a\text{ student earns a grade of B)=}\frac{number\text{ of students that earn grade B}}{Total\text{ number of students}} \\ Pr(a\text{ student earns a grade of B)=}\frac{10}{35} \\ \\ Pr(a\text{ student earns a grade of C)=}\frac{\text{number of students that earn grade C}}{Total\text{ number of students}} \\ Pr(a\text{ student earns a grade of C)=}\frac{15}{35} \end{gathered}[/tex]Therefore, the probability that a student earns a grade of A, B or C=
Pr(a student earns a grade of A) + Pr(a student earns a grade of B) + Pr(a student earns a grade of C).
This becomes;
[tex]\frac{5}{35}+\frac{10}{35}+\frac{15}{35}=\text{ }\frac{30}{35}=\frac{6}{7}[/tex]Hence, the probability that a student earns a grade of A, B or C is
[tex]\frac{6}{7}=0.86\text{ (to the nearest hundredth)}[/tex]