Question

the members of 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%

Explanation:

Step1: Calculate total number of students surveyed

The total number of students surveyed is the sum of all the values in the Venn - diagram regions, i.e., \(32 + 12+25 + 6=75\).

Step2: Calculate the value of \(a\) (students who like blue only or both)

The number of students who like blue (blue - only or blue and gold) is \(32 + 12=44\). The relative frequency \(a=\frac{44}{75}\times100\%\approx59\%\) (this is wrong, let's correct). The number of students who like blue only is 32. So \(a=\frac{32}{75}\times 100\%\approx43\%\).

Step3: Calculate the value of \(b\) (students who like gold only or both)

The number of students who like gold (gold - only or blue and gold) is \(25 + 12=37\). The relative frequency \(b=\frac{37}{75}\times100\%\approx49\%\) (wrong, correct way). The number of students who like gold only is 25. So \(b = \frac{25}{75}\times100\%\approx33\%\).

Answer:

a = 33%, b = 43%