Question

venn diagram 2
venn diagram 3
venn diagram 4

a class of 30 students took midterm science exams. 20 students passed the chemistry exam, 14 students passed physics, and 6 students passed both chemistry and physics. which venn diagram correctly represents this information?

• venn diagram 1
• venn diagram 2
• venn diagram 3
• venn diagram 4

Explanation:

⚡ Using what you learned: Venn Diagrams in Probability

Step 1: Identify the intersection

The number of students who passed both chemistry and physics goes in the overlapping region of the two circles:

$$ \text{Intersection } (C \cap P) = 6 $$

Step 2: Calculate the chemistry-only region

Subtract the overlapping students from the total who passed chemistry:

$$ C \text{ only} = 20 - 6 = 14 $$

Step 3: Calculate the physics-only region

Subtract the overlapping students from the total who passed physics:

$$ P \text{ only} = 14 - 6 = 8 $$

Step 4: Identify the matching diagram

The correct diagram must have:

• \( 14 \) in the left section (Chemistry only)
• \( 6 \) in the middle section (Both)
• \( 8 \) in the right section (Physics only)

This matches Venn diagram 2.

Answer:

Venn diagram 2