Question

a court record search of 265 incoming first - year students at a state university shows that 23 had been arrested at some point for underage drinking but not drug possession, and 15 had been arrested for possession but not underage drinking. there were 220 that had been arrested for neither. (a) construct a venn diagram illustrating these results.

Explanation:

Step1: Calculate total with at least one arrest

Total students: $265$. Students with neither arrest: $220$.
Expression: $265 - 220 = 45$

Step2: Calculate overlap of both arrests

Underage only: $23$, drug only: $15$. Total with one arrest: $23+15=38$.
Expression: $45 - 38 = 7$

Step3: Assign values to Venn regions

• Outside both circles (neither): $220$
• Underage only (red only): $23$
• Drug only (blue only): $15$
• Overlap (both): $7$

Answer:

The Venn diagram values are:

• Outside both circles: 220
• Underage drinking only (red circle non-overlap): 23
• Overlap of both circles: 7
• Drug possession only (blue circle non-overlap): 15