Question

Only tenth-, eleventh-, and twelfth-grade students attend Washington High School. The ratio of tenth graders to the school's total student population is $86:255$, and the ratio of eleventh graders to the school's total student population is $18:51$. If $1$ student is chosen at random from the entire school, which grade is that student most likely to be in?

• A. Tenth
• B. Eleventh
• C. Twelfth
• D. All grades are equally likely
• E. Cannot be determined from the given information

Answer 1

The correct option is B Eleventh

The ratio of tenth graders to the school's total population is $86:255=33.7\%$.

The ratio of eleventh graders to the school's total population is $18:51=35.3\%$.

Since the probability of a student being in either tenth, eleventh, or twelfth grade $=1=100\%$ (that is, certainty), then the probability of a randomly drawn student being in twelfth grade is $(100-33.7-35.3)=\mathrm{31.0.}$$\%$

When randomly choosing one student from the whole school, it is most likely $\left(35.3\%\right)$ that the student is in the eleventh grade.