Question

out of 25 students taking a midterm psychology exam, 17 answered the first of two bonus questions, 11 answered the second bonus question, and 2 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.
Total students: $n(U)=25$, $n(A)=17$, $n(B)=11$, $n(\text{neither})=2$.
First find $n(A\cup B)=25-2=23$.
Use $n(A\cup B)=n(A)+n(B)-n(A\cap B)$:
$23=17+11-n(A\cap B)$
$n(A\cap B)=17+11-23=5$

Step2: Find only first question

Students who answered only $A$: $n(A)-n(A\cap B)$
$17-5=12$

Step3: Find only second question

Students who answered only $B$: $n(B)-n(A\cap B)$
$11-5=6$

Step4: Verify Venn diagram sections

• Outside both circles (neither): 2
• Only first bonus circle: 12
• Overlap (both): 5
• Only second bonus circle: 6

Answer:

Venn diagram sections (rounded to nearest percent, or raw counts):

• Only "First bonus question": 12 (48%)
• Overlap (both questions): 5 (20%)
• Only "Second bonus question": 6 (24%)
• Outside both (neither): 2 (8%)