Question

out of 20 students taking a midterm psychology exam, 13 answered the first of two bonus questions, 11 answered the second bonus question, and 1 didnt bother with either one. round your answer to the nearest percent. part: 0 / 3 part 1 of 3 (a) construct a venn diagram illustrating these results.

Explanation:

Step1: Find students who answered both

Let $A$ = first bonus question, $B$ = second bonus question. Use principle of inclusion-exclusion:
$|A \cup B| = |A| + |B| - |A \cap B|$
We know $|A \cup B| = 20 - 1 = 19$, $|A|=13$, $|B|=11$.
$19 = 13 + 11 - |A \cap B|$
$|A \cap B| = 13 + 11 - 19 = 5$

Step2: Find only first bonus question

Subtract both from first question count:
$|A| - |A \cap B| = 13 - 5 = 8$

Step3: Find only second bonus question

Subtract both from second question count:
$|B| - |A \cap B| = 11 - 5 = 6$

Step4: Find neither bonus question

Given directly: $1$

Answer:

Venn diagram values:

• Region outside both circles (neither): $1$
• Only first bonus question circle: $8$
• Overlap of both circles (both): $5$
• Only second bonus question circle: $6$

As percentages (rounded to nearest percent):

• Neither: $\frac{1}{20} \times 100 = 5\%$
• Only first bonus: $\frac{8}{20} \times 100 = 40\%$
• Both bonus questions: $\frac{5}{20} \times 100 = 25\%$
• Only second bonus: $\frac{6}{20} \times 100 = 30\%$