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 a student is selected at random from the entire school, the grade in which the student is most likely to be is:

• 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:

$\frac{86}{255}=33.7$%

The ratio of eleventh graders to the school's total population is:

$\frac{18}{51}=35.3$%

Since the probability of a student being in either tenth, eleventh, or twelfth grade $=1=100$%, then the probability of a randomly drawn student being in twelfth grade is

$(100-33.7-35.3)$%$=31.0$%

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