Question

venn diagram 1

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 problem states that \( 6 \) students passed both chemistry (\( C \)) and physics (\( P \)). This value must go in the overlapping region (intersection) of the two circles.

$$ C \cap P = 6 $$

This rules out Venn diagram 1, which shows no overlap.

Step 2: Calculate the exclusive regions

To find the number of students who passed only chemistry, subtract the overlapping students from the total who passed chemistry:

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

To find the number of students who passed only physics, subtract the overlapping students from the total who passed physics:

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

Step 3: Calculate the outside region

To find the number of students who passed neither exam, subtract all students inside the circles from the total class size of \( 30 \):

$$ \text{Total inside} = 14 + 6 + 8 = 28 $$

$$ \text{Neither} = 30 - 28 = 2 $$

Venn diagram 2 correctly displays:

• \( 14 \) in the chemistry-only region
• \( 6 \) in the intersection
• \( 8 \) in the physics-only region
• \( 2 \) in the outside region

Answer:

Venn diagram 2