Question

A high school band asked a number of students whether they would like blue, gold, or both for the uniforms for the band. The results are given in the Venn diagram. What are the values of a and b in the relative frequency table for the survey results? Round answers to the nearest percent. a = 33%, b = 73% a = 68%, b = 43% a = 25%, b = 32% a = 33%, b = 43%

Answer 1

Given a Venn diagram showing the number of students that like blue uniform only as 32, the number of students that like gold uniform only as 25, the number of students that like blue and gold uniforms as 12 and the number of students that like neither blue nor gold uniform as 6.

Thus, the total number of students interviewed is 75.

Recall that relative frequency of an event is the outcome of the event divided by the total possible outcome of the experiment.

From the relative frequency table, a represent the relative frequency of the students that like gold but not blue.
From the Venn, diagram, the number of students that like gold uniform only as 25, thus the relative frequency of the students that like gold but not blue is given by
$\frac{25}{75} = \frac{1}{3}=0.33=33\%$

Therefore, a = 33% to the nearest percent.

Similarly, from the relative frequency table, b represent the relative frequency of the students that like blue but not gold.
From the Venn, diagram, the number of students that like blue uniform only as 32, thus the relative frequency of the students that like gold but not blue is given by
$\frac{32}{75} = 0.427=42.7\%$

Therefore, b = 43% to the nearest percent.